Modeling Available Soil Moisture Application Note

Transcription

1 Modeling Availale Soil Moiture Application Note Gaylon Campell, Ph.D METER Group, Inc. (Formerly Decagon Device, Inc.) Pullman, WA Both the amount and the availaility of water in oil i important to plant root and oil dwelling organim. To decrie the amount of water in the oil we ue the term water content. To decrie the availaility we talk of water potential. In thermodynamic the water content would e referred to a the extenive variale and the water potential a the intenive variale. Both are needed to correctly decrie the tate of water in oil and plant. In addition to decriing the tate of water in the oil, it may alo e neceary to know how fat water will move in the oil. For thi we need to know the hydraulic conductivity. Other important oil parameter are the total pore pace, the drained upper limit for oil water, and the lower limit of availale water in a oil. Since thee propertie vary widely among oil, it would e helpful to etalih correlation etween thee very ueful parameter and eaily meaured propertie uch a oil texture and ulk denity. Thi document will preent the information needed for imple model of oil water procee. Water Content and Bulk Denity The amount of water in oil i decried a the water content. Thi can e decried on either a ma or a volume ai. The ma ai water content i the ma of water lot from a oil ample when it i dried at 105 C divided y the ma of the dry oil. Thi definition i ueful for determining the water content in the laoratory, ut i not particularly ueful for decriing the amount of water in the field. There, the volume ai water content i more ueful. It i the volume of water held in unit volume of oil. If w i the ma ai water content and θ i the volume ai water content, then w θ = (1) w where and w are the ulk denity and the denity of water. The ulk denity of the oil i the dry oil ma divided y the oil volume. The water denity i 1 Mg/m 3. In mineral oil the ulk denity typically ha a value etween 1.1 and 1.7 Mg/m 3. The volumetric water content i therefore typically larger than the ma water content. You can think of θ a the fraction of the oil volume taken up y water. The fraction taken up y olid can e computed from the ulk denity: f = (2) where i the denity of the oil olid. It typically ha a value around 2.65 Mg/m 3. The total pore pace in the oil i 1 f. When the oil i completely aturated with water, it water content i the aturation water content,. It can e calculated from the ulk denity a: θ 1 f = 1 (3) = Water Potential All water held in oil i not equally availale to plant, microe and inect. One meaure of availaility i the water potential. Water potential i the potential energy per unit ma of water of the water. The water in the oil i held y force of adheion to the oil matrix, i uject to gravitational attraction, and contain olute which lower it energy compared to the energy of pure, free water. Living organim mut therefore expend energy to remove water from the oil. The water potential i a meaure of the energy per unit ma of water which i required to remove an infiniteimal quantity of water from the oil and tranport it to a reference pool of pure free water. Becaue energy i uually required to remove water, water potential i uually a negative quantity. For potential energy per unit ma, the unit of water potential are 3 2 J/kg. Energy per unit volume come out J/m 3, or C

2 N/m or Pa. We trongly favor J/kg, ut one frequently ee water potential reported in kpa or MPa. One J/kg i numerically almot equal to 1 kpa. While many factor influence the water potential, the mot important in a iological context i uually the matric potential. It arie ecaue of the attraction of the oil matrix for water, and i therefore trongly dependent on the propertie of the matrix and the amount of water in the matrix. Figure 5.1 how typical moiture releae curve or moiture characteritic for and, ilt and clay oil. Clay, ecaue of their maller pore ize and greater particle urface area, lower the water potential more at a given water content, than do and and loam oil. Moiture characteritic like thoe in Fig. (1) are linear when the logarithm of water potential i plotted a a function of the logarithm of water content. The equation decriing thee curve i: θ ψ m = ψ c (4) θ where ψ m i matric potential, θ i volumetric water content, ψe i called the air entry potential of the oil, and i a contant. The air entry potential and aturation water content are ometime comined into a ingle contant a, giving m - ψ = aθ (5) o a = ψ e θ (5.5) Figure 1 Soil moiture characteritic for three different oil type The air entry potential and the value depend on the texture and tructure of the oil. Soil texture can e pecified uing the name of a textural cla, uch a ilt loam or fine andy loam, a fraction of and, ilt and clay, or a a mean particle diameter and a tandard deviation of particle diameter. The latter i the mot ueful for determining hydraulic propertie. We will ue the ulk denity or total pore pace a a meaure of oil tructure. Shiozawa and Campell (1991) give the following relationhip for converting meaurement of ilt and clay fraction to geometric mean particle diameter and tandard deviation: and d g = exp( m t m y ) (6) σ g = exp{[ m t m y (ln d g ) 2 ] 1/2 } where m t and m y are the fraction of ilt and clay in the ample, d g i the geometric mean particle diameter in µm, and σ g i the geometric tandard deviation. The relationhip etween hydraulic propertie and the oil texture and tructure are, at preent, quite uncertain, even though a lot of reearch ha een done in thi area. The following are equation derived partially from theory and partially y empirically fitting data et from a numer of location. The dependence of air entry potential on texture and ulk denity can e computed from: LOGGERS 2

3 where θ i from eq. 3 and d g i from eq. 6. The exponent, can e etimated from 5 5 ψ e = 2 1 = (2θ ) (7) d g d g 10 = + 0.2σ g (8) d g Tale 1 lit the 12 texture clae of oil and give the approximate ilt and clay fraction for the center of each cla. It then how the value for d g, σ g, ψe, and for each cla. Field Capacity and Permanent Wilting Point Water move rapidly through oil at high water content, mainly ecaue of the downward pull of gravity and the high hydraulic conductivity of nearly aturated oil. A water drain from the oil, however, the hydraulic conductivity decreae rapidly and the rate of movement low. The downward movement of water under the influence of gravity ecome very mall at water potential etween -10 and -33 J/kg. Water at potential elow thee value i therefore held within the root zone and i availale for plant uptake. The water content when the matric potential i etween -10 and -33 J/kg (-10 for and; -33 for clay) i the field capacity water content (θ fc ), or the drained upper limit. Thi i the water content one would expect to find if a oil profile were wet y a heavy rain or irrigation, covered, and allowed to tand for two or three day. In other word, it i the highet water content one would typically expect to find in a field oil except right after water i added. Value of the water content at -33 J/kg were computed uing eq. 4 for each of the texture, auming = 0.5, and are hown in Tale 1. Note that and drain to jut a few percent moiture at field capacity, while finer texture oil may have water content aove 0.3 m 3 m -3. Note, however, that all field capacity water content are well elow aturation. The value hown in the tale may need to e adjuted to repreent what one would find in the field ecaue the ulk denity tend to e texture dependent. Sand tend to have high ulk denitie (1.6 Mg/m) while finer textured oil tend to have lower ulk denitie. Permanent wilting doe not mean that the plant i killed y water potential in thi range. It mean that the plant will not recover from wilting unle water i applied. Many pecie are ale to withdraw water from oil to water potential well elow J/kg, and rapid withdrawal of water from the oil will make water unavailale to the plant which i held at potential well aove J/kg. The value doe, however, provide an approximate lower limit for the water content of oil from which plant are extracting water. Value of θ pwp are alo hown in Tale 1 for θ = 0.5. Tale 1 Phyical and hydraulic propertie of oil according to oil texture. The ilt and clay fraction are mid-range value for each textural cla. The hydraulic propertie were computed uing the equation from the text auming θ = 0.5 for all texture. Texture Silt Clay dg ( g e (J/kg k (kg m -3 ) av Sand Loamy and Sandy loam Sandy clay loam Loam Sandy clay Silt loam Silt e LOGGERS 3

4 Texture Silt Clay dg ( g e (J/kg k (kg m -3 ) av Clay loam e Silty clay loam e Silty clay e Clay e Plant availale water i defined a the water held in the oil etween field capacity and permanent wilting. Thee value are alo hown in Tale 1. The value are low for coare-textured oil, ut tend to e quite uniform for other oil texture, even though the field capacity and permanent wilting point value vary widely. A note of caution i in order though in uing the value given in the tale. Predicting PWP from Field Capacity Since oth field capacity and permanent wilting point can e computed from aic oil parameter, it tand to reaon that they would e correlated. Figure 2 how the permanent wilt water content for all 12 texture clae plotted a a function of the field capacity water content. The correlation i good, and the data are fit well y a econd order polynomial. The practical outcome of thi i that one need only know one or the other of thee variale, and the other can e found from the relationhip etween the two. Figure 2 Permanent wilt water content a a function of field capacity water content for the 12 texture clae hown in Tale 1. Otaining Hydraulic Propertie from Soil Survey Data The -33 and J/kg (1/3 and 15 ar) water content are often availale from oil urvey data. If they are known, we can find a and in eq. (5.5). Taking logarithm of oth ide in eq. (5.5), we otain ln ψm = ln a- lnθ. Sutituting θ fc = 33 and θ pwp = 1500, and their correponding water content (ue poitive numer for ψm when you take log; you can't take the log of a negative numer) you get two equation in two unknown, and a, which you can olve imultaneouly to get the two parameter: ln1500 ln 33 = (9) ln θ ln fc θ pwp a = exp(ln33 + ln fc ) (10) Make ure the value of θ fc and θ pwp that you ue are volumetric water content. Mot laoratory data are ma ai water content ecaue they are meaured uing oven drying. If they are ma ai water content, convert them to volume ai water content uing the ulk denity and eq. 1 efore uing them to compute a and LOGGERS 4

5 Sometime all one ha i an etimate of availale water content ford a oil. In thi cae, we can etimate ufficiently accurately to till find a value for a. Let θ av = θ fc - θ pwp, e the availale water content for the oil. We can rearrange eq. (5) to otain a = ψ -1/ fc θ av ψ -1/ pwp 5 If we have no other information to indicate the value for, we will aume a value of 5. Thi give a = 637θ av. Knowing value for a and, we can ue eq. (5) to find θ fc and θ pwp. An etimate of air dry water content, which we will need in model of evaporation from oil urface, i etimated from (11) θ pwp θ d = (12) 3 Reference 1. Campell, G. S. (1985) Soil Phyic with BASIC: Tranport Model for Soil-Plant Sytem. Elevier, Amterdam. 2. Shiozawa, S. and G. S. Campell (1991) On the calculation of mean particle diameter and tandard deviation from and, ilt, and clay fraction. Soil Sci. 152: LOGGERS ( ) C