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Agron. Physiol. Lab., P.O. Box 110965, Univ. of Florida, Gainesville, FL 32611-0965
* Corresponding author (trsincl{at}ifas.ufl.edu)
Received for publication November 21, 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: FTSW, fraction of transpirable soil water • RT, relative daily transpiration rate
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The difficulty with the thermodynamic characterization of water deficits was that no unique functions were found to describe plant response to either soil or plant water potential. Sinclair and Ludlow (1985) argued that, in fact, plants were not directly sensitive to water potential, and they suggested that sensors in plants associated with volume and/or turgor changes were likely responsible for physiological responses. Ritchie (1981) suggested a return to the earlier perspective of quantitatively expressing plant response based on expressions of volumetric available soil water. By normalizing the available soil water content of soils, Ritchie (1981) suggested that there might be a response function that was common to most soils. Indeed, an increasing number of studies involving a range of crop species have now shown consistently that a two-segment model based on available soil water describes well the changes in daily plant gas exchange rate in response to soil drying (Sadras and Milroy, 1996). For most conditions, daily plant gas exchange rate is unchanged until about two-thirds of the available water is lost in the first segment of the model. The second segment is a linear decline in daily gas exchange rate until the available water is exhausted.
The basis for the nearly universal response of daily transpiration rates to soil drying based on normalized available soil water content during a period of prolonged soil drying is unexplained. One possibility is that plants have a physiological mechanism to detect normalized volumetric soil water content, and this mechanism triggers changes in plant behavior. There is no evidence for such a direct sensory system in plants linked directly to volumetric soil water content. An alternate hypothesis is that the flux of water from the soil to the plant when viewed on the time scale of daily time steps is associated with volumetric water content of the soil, and the decrease in water flux triggers physiological adjustments in the plant. Certainly, water flux in the soil can depend on soil water content when soil hydraulic conductivity decreases to levels where water movement is severely restricted (Gardner, 1960; Cowan, 1965; Sperry et al., 1998).
Previous analyses of plant responses to soil drying have focused on characterizing soil water status based on thermodynamic water potential and do not allow ready interpretation based on changes in volumetric water content. There is no basis to relate directly the observations on plant response to volumetric soil water content, nor to resolve the apparent insensitivity in the pattern of relative plant gas exchange rate on drying soil to a number of variables that influence plant gas exchange rate. The objective of this study, therefore, was to undertake a theoretical analysis of water flux in the soil–plant system to develop a possible link between water flux in the plant–soil system to changes in available soil water and soil hydraulic conductivity. Transpiration rates for 11 soils were calculated as functions of extractable soil water content.
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MODEL DEVELOPMENT |
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TOPABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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 | [1] |
root surf = hydrostatic water pressure at root surface (MPa), and leaf = hydrostatic pressure in leaves during period of active transpiration (MPa).
Equation [1] assumes that there is no net change in plant water storage so that water movement in the plant (E) is matched by water transport from the bulk soil to the root surface. In his classic analysis, Cowan (1965) derived the following expression (his Eq. [19] converted to units of MPa from cm water) to describe the hydrostatic pressure gradient (again, assuming no osmotic gradient) between the bulk soil (soil) and root surf.
 | [2] |
= variable for geometry of soil water extraction around roots (cm2), Q = average daily rate of volumetric decrease in soil water content (cm3 cm–3 d–1), and K = soil hydraulic conductivity (cm d–1).
The variable derived by Cowan (1965) is a complex expression (his Eq. [17]) reflecting the extraction of water from concentric cylindrical shells in the soil surrounding roots. The value of depends on the radius of the roots (rroot, cm) and the radius of the cylinder of soil water extraction associated with each root (rsoil, cm). Assuming a uniform distribution of roots in the soil, rsoil can be approximated from root length density (L, cm cm–3) by the following relationship:
 | [3] |
An assumption in Cowan's derivation is that the ratio of rsoil to rroot is less than 16. Consequently, for roots of radius 0.05 cm, the value of rsoil must be less than 0.8 cm, which is equivalent to a root length density greater than 0.5 cm cm–3. Therefore, the estimates of are appropriate over much of the range of root length densities expected in the soil water extraction zone of crops.
There is a large range of possible values for . For example, values of root length density equal to 4 cm cm–3 (rsoil = 0.28 cm) and rroot = 0.05 cm result in = 0.04 cm2 while a root length density of 0.5 cm cm–3 (rsoil = 0.78 cm) and the same rroot result in a value for of 0.62 cm2. The value of for much of this analysis was assumed to be 0.15 cm2, which is appropriate for rroot = 0.05 cm and rsoil = 0.45 cm (root length density = 1.52 cm cm–3), for example. As discussed later, the derived water loss response shows little sensitivity to the value assumed for .
The mean value of Q in Eq. [2] can be approximated by
 | [4] |
Replacing root surf in Eq. [1] by the definition given in Eq. [2] and including the definition of Q from Eq. [4] results in the following equation:
 | [5] |
 | [6] |
The daily transpiration rate of a plant subjected to drying soil (Eq. [6]) can be normalized with respect to the transpiration rate of a well-watered plant of the same size and stage of development. This normalization, therefore, generates an expression for relative daily transpiration rate (RT), which is the variable reported in much of the experimental literature. The value of Ew was set equal to 0.8 cm d–1 in most of the following analyses as a reasonable upper limit for daily water loss rate. Again, it will be shown that the actual value selected for Ew has virtually no influence on the calculation of RT.
Assuming that under well-watered conditions, root surf is near zero, then from Eq. [1], Ew simply equals (–Cplant x leaf). Further, it will be assumed that Cplant does not change to a large extent until soil drying becomes severe (Bristow et al., 1984). This assumption, therefore, means that in this analysis, the changes in RT with soil drying are examined solely as possible responses to changes in soil water content. These assumptions result in the following expression for RT:
 | [7] |
soil and K vary as soil water content changes, Eq. [7] yields a hypothesis for expressing RT as a function of soil water content. The large decreases in K associated with soil drying, in particular, would seemingly have a large influence on RT.
Soil Characteristics
The objective of this analysis was to express RT as a function of soil volumetric water content within the range of plant-available volumetric soil water content. Therefore, it is necessary to analyze Eq. [7] by expressing the variables soil and K as functions of volumetric soil water content. The dependence of these variables on volumetric soil water (
, cm3 cm–3) can be expressed by the following empirical equations (Clapp and Hornberger, 1978):
 | [8] |
*soil = soil water potential at saturation (MPa), sat = volumetric water content at saturation (cm3 cm–3), and b = empirical constant for each soil, and
 | [9] |
Since b has values ranging from 4.05 to 11.4 for differing soils (Table 1), Eq. [9] reflects the decrease in K over several orders of magnitude as decreases.
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using Eq. [8] and [9]. The focus of this analysis is to calculate RT in the range of available to the plant to support transpiration. Therefore, RT is calculated between the upper and lower limits of soil water available to support plant transpiration expressed as volumetric soil water-holding capacity. The lower limit of available soil water for transpiration was defined as the volumetric soil water content where RT decreases to less than 0.1 (Sinclair and Ludlow, 1986). Therefore, the volumetric water content of the lower limit was calculated using Eq. [7] for each of 11 soils using the criterion of RT < 0.1 (Table 1). The upper limit of available soil water was found by Ratliff et al. (1983) to be about 0.13 cm3 cm–3 greater than the lower limit for most soils. The exceptions in the 0.13 cm3 cm–3 difference in available soil water were for sand and silt in which the upper limit was 0.08 cm3 cm–3 and 0.15 cm3 cm–3 greater than the lower limit, respectively. In the initial calculations of RT, the volumetric water content at the upper limit of all 11 soils was simply assumed to be 0.13 cm3 cm–3 greater than the lower limit.
The total amount of soil water available to support leaf gas exchange was defined by Sinclair and Ludlow (1986) as the "transpirable soil water" and the relative dryness of the soil between the two limits was the "fraction of transpirable soil water" (FTSW). By definition, FTSW has a value of 1.0 at the upper limit and 0.0 at the lower limit. In these calculations, RT was calculated for each soil between the lower and upper limits at 0.05 FTSW increments.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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leaf. To complicate matters, leaf is highly dynamic under natural conditions because it is responsive to both soil drying and transpiration rate. Since the focus of this analysis was to determine the impact of once the soil was sufficiently dry to influence plant behavior, it was assumed that leaf could be represented by a fixed minimum value. The sensitivity of RT to leaf was tested by setting leaf equal to –1.0, –1.5, or –2.0 MPa. The results for the silty clay loam soil, shown in Fig. 1
, illustrate the shift in the response curve. Relative transpiration rates decreased at higher FTSW when leaf was set to –1.0 MPa and at lower FTSW as compared with the –1.5 MPa case. Setting leaf equal to –2.0 MPa caused the RT decrease to occur at lower FTSW as compared with the –1.5 MPa case. These responses are similar to those presented by Cowan (1965)(Fig. 8).
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leaf in the calculation of RT, however, are no longer consistent with the original definition of the lower endpoint for transpirable soil water. That is, in the calculation of RT, the volumetric soil water content for the lower endpoint of transpirable soil water needs to be shifted when the value of leaf is different from –1.5 MPa. Consequently, a key impact of changing leaf was that the amount of water available to the plant was changed. In the calculations in Fig. 1, the range of volumetric transpirable soil water has to be decreased for plants when leaf is increased to –1.0 MPa to be consistent with the definition of transpirable soil water. Conversely, volumetric transpirable soil water needs to be increased when leaf is decreased –2.0 MPa. For the silty clay loam soil, the volumetric endpoint of 0.221 cm3 cm–3 calculated for when leaf equals –1.5 MPa was recomputed based on the criterion of RT < 0.1 and found to be 0.234 cm3 cm–3 when leaf is assumed equal to –1.0 MPa and 0.213 cm3 cm–3 when leaf equals –2.0 MPa.
Recalculation of the RT response is also shown in Fig. 1 for the cases where the range of transpirable soil water was decreased to 0.12 cm3 cm–3 for leaf of –1.0 MPa and increased to 0.14 cm3 cm–3 for leaf of –2.0 MPa. These adjustments in the amount of transpirable soil water, which are implicit in the experimental protocol, resulted in theoretical response curves that were essentially identical to the original calculations of RT obtained by assuming leaf equals –1.5 MPa. Based on this theoretical analysis, it appears that the experimental response of RT expressed as a function of FTSW is not sensitive to variations in the leaf to which different plant species dry.
The remaining variables defining RT in Eq. [7] are all collected in a single term [Ew/(1000dK)]. For wet soil, this term has a very small value on the order of 10–5 MPa. Since leaf is subtracted from this term, the value of one of these variables has to change by at least four orders of magnitude before there is any appreciable influence on RT. Not surprisingly, any variations in Ew and d over a wide range of assumed values were found to have no influence on RT.
Ray et al. (2002) attempted to examine the changes in the threshold for RT decline of maize (Zea mays L.) plants as influenced by transpiration rate (Ew). They subjected plants to different atmospheric vapor pressure deficit environments over a range from 1.1 to 3.6 kPa in an attempt to alter transpiration rate, but these treatments resulted in only modest differences in transpiration rate (37%). The imposed variation in transpiration rates had no consistent influence on the RT threshold in their soil-drying experiment. The predicted lack of sensitivity in Eq. [7] to variation in Ew is consistent with these experimental results.
Root length density intuitively seems as if it could have a large influence on the response of RT to drying soil. The influence of L on RT is expressed in Eq. [7] through the variable . A sensitivity test was done by varying over a 30-fold range from 0.02 to 0.60 cm2 (L = 6.3 to 0.5 cm cm–3, respectively, when rroot = 0.05 cm). The 30-fold range in was found to have virtually no influence on the RT response curve as anticipated by the previous discussion of the sensitivity of the term in which is expressed.
Although the variable K changes by about four orders of magnitude with soil drying, this large change by itself has a fairly modest influence on RT as calculated in Eq. [7]. For example, decreasing K from 0.2 cm d–1 for wet soil to 2 x 10–5 cm d–1 for dry soil results in an increase in the Ew/(1000dK) term in Eq. [7] from 10–5 MPa to 0.1 MPa. As compared with the leaf of –1.5 MPa, even this large change in K has only a modest influence on RT.
Consequently, an approximation of Eq. [7] can be written by eliminating the Ew/(1000dK) term and including the definition of soil given in Eq. [8]
 | [10] |
Response to Soil Drying
The daily transpiration response to soil drying was calculated as a function of volumetric soil water content for each of 11 soils using Eq. [7]. Soil drying, as reflected by decreasing FTSW, resulted in a consistent pattern in the changes in RT across all 11 soil textures (Fig. 2)
. There was a broad range when the soil was relatively wet, over which there was only a small change in RT. When the soil dried to FTSW values of roughly 1/3, the decrease in RT became much greater. This threshold level of FTSW was the soil water content where soil began to decrease substantially for all soils. As the soil continued to dry, there were greater decreases in RT, and soil, down to FTSW = 0 where RT was defined as being less than 0.1.
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Figure 2 does indicate, however, some differences among the various soils in the RT response to soil drying, which differs from the general observation that the response varies little among soil textures. An experimental exception was reported for sands where the threshold for decline in RT was at unusually low FTSW threshold values for two sandy soils (Sinclair et al., 1998) similar to the results shown for sandy soils in Fig. 2.
Differences, however, among soils in their RT pattern can be resolved by accounting for possible differences in available soil water among soil textures. It was previously assumed for all soils that the volumetric water content range of available soil water was 0.13 cm3 cm–3. The results of Ratliff et al. (1983) indicated that the 0.13 cm3 cm–3 value is high for sandy soils and somewhat low for a silt soil. Values for RT were recomputed by assuming that the range of available soil water was only 0.10 cm3 cm–3 for three sandy soils and 0.15 cm3 cm–3 for the silt loam soil. The adjustment in available soil water for these four soils caused all soils to coalesce into nearly a common curve (Fig. 3) . Hence, scaling FTSW to the appropriate range of transpirable soil water for each soil supports the existence of a common response in RT to decreasing FTSW.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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This derivation of an expression to describe RT based on volumetric soil water content (Eq. [7]) indicates remarkable insensitivity to a number of plant and soil variables, as has been observed experimentally. The expression is essentially independent of moderate changes in root length density, transpiration rate, and soil depth. Changes in soil conductivity also have only a small influence on RT. Across all soil textures, this analysis indicated that the response of RT to soil drying as a function of FTSW had roughly the same response (Fig. 2). While most soils have roughly the same storage capacity for transpirable soil water, accounting for possible differences among soil textures in available soil water results in further coalescence of the response curves (Fig. 3).
One consequence of this derivation describing changes in daily transpiration rate in response to soil drying is that there appears to be few alternatives for physiologically modifying plants to alter gas exchange response when grown on uniformly drying soil. Certainly, this analysis does not indicate any plant adjustments that will shift the threshold for declining relative transpiration to lower soil water contents. On the other hand, a threshold for the decline in RT at high FTSW as a result of active plant control may be physically possible, but such a control requires a sensory system to detect decreasing water content of the soil while the plant is still being supplied with water at rates essentially adequate to fully meet maximum transpiration requirements. Overall, the stability in the response of daily transpiration rate to changes in volumetric soil water content commonly reported for differing plant species grown under a wide range of conditions appears to be explained in large part by the derived hypothesis.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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This article has been cited by other articles:
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  K. Metselaar and T. R. Sinclair Comment on "Theoretical Analysis of Soil and Plant Traits Influencing Daily Plant Water Flux on Drying Soils" by T.R. Sinclair. Agron. J. 97:1148-1152 (2005) Agron. J., June 26, 2007; 99(4): 1188 - 1189. [Full Text] [PDF]
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 K. Metselaar and Q. de Jong van Lier The Shape of the Transpiration Reduction Function under Plant Water Stress Vadose Zone J., January 24, 2007; 6(1): 124 - 139. [Abstract] [Full Text] [PDF]
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