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Comparison of the root water uptake term of four simulation models

Profile image of Marius HeinenMarius Heinen

2011, Atmospheric Chemistry and Physics

Abstract

Willigen P. de, J.C. van Dam, M. Javaux and M. Heinen, 2011. Comparison of the root water uptake term of four simulation models. Wageningen, Alterra, Alterrareport 2206. 66 pp.; 24 fig.; 8 tab.; 31 ref.

Figures (41)
References for description an applications of the models. Table 1 We particularly investigate how the four models cope with hydraulic lift compensation mechanisms and effect of soil on uptake. With hydraulic lift we mean root water excretion, when the xylem pressure heads exceeds the pressure head at the root-soil interface. So hydraulic lift may also denote downward movement of water by the root system. Each of these models also differ by its intrinsic complexity. The importance of such a complexity against modeling performances is also assessed in this report. For the comparison three scenarios will be considered. In the first one we check whether the models concerned do give similar results with respect to the basic processes of soil water flow. The other two scenarios specifically aim at comparing the respective water uptake routines. In recent years the increasing computational capacity and development of microscopic measurement techniques for root water uptake create avenues for an even more detailed physical based modeling approach. A clear example is the RSWMS model (Javaux et al., 2008) which accommodates 3-dimensional rooting patterns with detailed water movement. RSWMS simulates 3-dimensional soil water flow, flow towards the roots, and radial and longitudinal flow inside the root system. This creates new research possibilities on the important feedback mechanisms occurring in the rhizosphere when soil moisture becomes limiting. In this report, we show the performance of various modeling concepts covering a broad range of assumptions for well-defined drought situations. Four models were involved in the comparison in the comparison, these are oiven hy their acrgnyme SWAP-macron SWAP-micro FIISSIM2 and RSWMS Table 1 oivec references for the
References for description an applications of the models. Table 1 We particularly investigate how the four models cope with hydraulic lift compensation mechanisms and effect of soil on uptake. With hydraulic lift we mean root water excretion, when the xylem pressure heads exceeds the pressure head at the root-soil interface. So hydraulic lift may also denote downward movement of water by the root system. Each of these models also differ by its intrinsic complexity. The importance of such a complexity against modeling performances is also assessed in this report. For the comparison three scenarios will be considered. In the first one we check whether the models concerned do give similar results with respect to the basic processes of soil water flow. The other two scenarios specifically aim at comparing the respective water uptake routines. In recent years the increasing computational capacity and development of microscopic measurement techniques for root water uptake create avenues for an even more detailed physical based modeling approach. A clear example is the RSWMS model (Javaux et al., 2008) which accommodates 3-dimensional rooting patterns with detailed water movement. RSWMS simulates 3-dimensional soil water flow, flow towards the roots, and radial and longitudinal flow inside the root system. This creates new research possibilities on the important feedback mechanisms occurring in the rhizosphere when soil moisture becomes limiting. In this report, we show the performance of various modeling concepts covering a broad range of assumptions for well-defined drought situations. Four models were involved in the comparison in the comparison, these are oiven hy their acrgnyme SWAP-macron SWAP-micro FIISSIM2 and RSWMS Table 1 oivec references for the
Variables and parameters considered in the water uptake routine of the different models Table 2
Variables and parameters considered in the water uptake routine of the different models Table 2
Reduction coefficient (a) as a function of pressure head (h) as used in SWAP-macro. The uptake rate is expressed in cm? cm? d?. The relation between / and a is shown in Figure 1
Reduction coefficient (a) as a function of pressure head (h) as used in SWAP-macro. The uptake rate is expressed in cm? cm? d?. The relation between / and a is shown in Figure 1
SO w,,iS almost proportional to root length density as the numerator of the RHS of Eq. (19) changes much aster with change in Z,, than the denominator. The highest possible uptake rate occurs when the pressure head at the root surface is that at wilting point. n that case the matric flux potential at the root surface is then zero by definition, see Eq. (10). If the corresponding uptake rate is greater than the required uptake rate the actual uptake rate is equal to the required uptake rate, else it equals the highest possible uptake rate. So the actual uptake rate of a single ayer can be formulated as:
SO w,,iS almost proportional to root length density as the numerator of the RHS of Eq. (19) changes much aster with change in Z,, than the denominator. The highest possible uptake rate occurs when the pressure head at the root surface is that at wilting point. n that case the matric flux potential at the root surface is then zero by definition, see Eq. (10). If the corresponding uptake rate is greater than the required uptake rate the actual uptake rate is equal to the required uptake rate, else it equals the highest possible uptake rate. So the actual uptake rate of a single ayer can be formulated as:
As mentioned in the context of Eq. (17) R, >> R,,s0 p° >>1, so that Note the similarity between Eq. (30) and Eq. (19). The constant in the second term of the denominator on the RHS of Eq. (19) is — a tale? = -1.55, almost the same as -1.5 in Eq. (30). The uptake rate can be made explicit from Eq. (27) yielding:
As mentioned in the context of Eq. (17) R, >> R,,s0 p° >>1, so that Note the similarity between Eq. (30) and Eq. (19). The constant in the second term of the denominator on the RHS of Eq. (19) is — a tale? = -1.55, almost the same as -1.5 in Eq. (30). The uptake rate can be made explicit from Eq. (27) yielding:
Equation (34) states that in the path soil - root surface - xylem there is no accumulation of water, Eq. (35) gives the relation between leaf and root potential, and Eq. (36) states that transport into the root equals actual transpiration. Because of the non-linearity of Eqs. (35) and (36) these equations have to be solved by iteration for the three unknowns /, (from which ®, follows) /,and #, for a given bulk pressure head /in the soil layer (from which ® follows). ey EE pr: fe PES eel | hd en Se ee eee! Med agate oceans cr gm | ceerren—er The calculations for a multilayer system proceed along the same lines. Details can be found in Appendix 1. Where #, is the leaf water pressure head (cm), /, is the root water pressure head (cm), 7, is the actual transpiration rate (cm d*), and Z, is the conductance in the path root to leaf (d). Details are found in Appendix |. The actual transpiration is a function of the potential transpiration and the leaf water potential, we used the approach of Campbell (1985, 1991) proposed, i-e.:
Equation (34) states that in the path soil - root surface - xylem there is no accumulation of water, Eq. (35) gives the relation between leaf and root potential, and Eq. (36) states that transport into the root equals actual transpiration. Because of the non-linearity of Eqs. (35) and (36) these equations have to be solved by iteration for the three unknowns /, (from which ®, follows) /,and #, for a given bulk pressure head /in the soil layer (from which ® follows). ey EE pr: fe PES eel | hd en Se ee eee! Med agate oceans cr gm | ceerren—er The calculations for a multilayer system proceed along the same lines. Details can be found in Appendix 1. Where #, is the leaf water pressure head (cm), /, is the root water pressure head (cm), 7, is the actual transpiration rate (cm d*), and Z, is the conductance in the path root to leaf (d). Details are found in Appendix |. The actual transpiration is a function of the potential transpiration and the leaf water potential, we used the approach of Campbell (1985, 1991) proposed, i-e.:
Relative transpiration as a function of plant water potential (Eq. (33). Parameters: q = 0.7, hy, 12 = 16600 cm. Summarizing: the FUSSIM2 water uptake routine does not merely take the soil properties into account, but also the plant properties as radial conductance, and plant conductance. The actual transpiration is a function of the leaf water potential.
Relative transpiration as a function of plant water potential (Eq. (33). Parameters: q = 0.7, hy, 12 = 16600 cm. Summarizing: the FUSSIM2 water uptake routine does not merely take the soil properties into account, but also the plant properties as radial conductance, and plant conductance. The actual transpiration is a function of the leaf water potential.
Domain and resolution details of the four models.
Domain and resolution details of the four models.
Mualem - van Genuchten parameters for three soils of the Dutch Staring series (Wosten et al., 2001)
Mualem - van Genuchten parameters for three soils of the Dutch Staring series (Wosten et al., 2001)
Architecture of a 45-d old Maize root system.
Architecture of a 45-d old Maize root system.
$2: The second root water uptake scenario is similar to S1, except that 1) precipitation did not occur, and 2) the transpiration during the day was distributed according to a sinusoidal pattern: 00:00 - 06:00, no transpiration; 06:00 - 18:00, transpiration following a (positive) sine curve (in total 4 mm d*); 18:00 - 24:00, no transpiration. This means that at 12:00 the potential transpiration demand is 12.6 mm d?, much larger than the average demand of 4 mm d" (Figure 4).
$2: The second root water uptake scenario is similar to S1, except that 1) precipitation did not occur, and 2) the transpiration during the day was distributed according to a sinusoidal pattern: 00:00 - 06:00, no transpiration; 06:00 - 18:00, transpiration following a (positive) sine curve (in total 4 mm d*); 18:00 - 24:00, no transpiration. This means that at 12:00 the potential transpiration demand is 12.6 mm d?, much larger than the average demand of 4 mm d" (Figure 4).
Model specific inout data with respect to root water extraction. Table 5
Model specific inout data with respect to root water extraction. Table 5
Figure 6 Diftusivity (solid lines) and volumetric water content (broken lines) as a function of absolute pressure head.
Figure 6 Diftusivity (solid lines) and volumetric water content (broken lines) as a function of absolute pressure head.
Scenario Check. Distribution of pressure head with depth at time = 0.5, 1 and 10 days. The lines pertain to FUSSIM2, the squares to SWAP and the triangles to RSWMS for the three soils Zandb3 (a), Kleib1 1 (b) and Leemb13 (c).
Scenario Check. Distribution of pressure head with depth at time = 0.5, 1 and 10 days. The lines pertain to FUSSIM2, the squares to SWAP and the triangles to RSWMS for the three soils Zandb3 (a), Kleib1 1 (b) and Leemb13 (c).
Pressure head distribution as calculated with RSWMS, after a dry spell of 15.5 days with a potential transpiration rate of 4 mm ad The previous two sections presented the different water uptake models in case of a single layer. It is also interesting to see how uptake is distributed over the root system for a given pressure head distribution. The model RSWMS was used to generate the pressure head profiles for the three soils after a dry period of 15.5 days, with a potential transpiration rate of 4 mm d?. This pressure head profile was used to calculate the corresponding water uptake distribution for the four models, employing the parameters given in Table 5. Figure 10 presents the pressure head profile for the three soil types and Figure 11 the computed relative root water uptake from the soil column. Note that only in the case of SWAP-macro the soils pressure head distribution has a direct relation to water uptake distribution. In the other three models the relation is indirect: in case of SWAP-micro via the pressure head at the soil-root interface (PHR), for FUSSIM2 via PHR, the root pressure head (PHX) and radial root resistance, and in RSWMS via PHR, PHX, root radial and axial resistance. The water uptake distribution of FUSSIM2 shows the largest differences between the three soils, which has to do with the fact that here in case of clay and loam hydraulic lift occurred in the upper 10-15 cm. The other models showed a similar pattern of uptake distribution for all three soils, especially in the case of RSWMS.
Pressure head distribution as calculated with RSWMS, after a dry spell of 15.5 days with a potential transpiration rate of 4 mm ad The previous two sections presented the different water uptake models in case of a single layer. It is also interesting to see how uptake is distributed over the root system for a given pressure head distribution. The model RSWMS was used to generate the pressure head profiles for the three soils after a dry period of 15.5 days, with a potential transpiration rate of 4 mm d?. This pressure head profile was used to calculate the corresponding water uptake distribution for the four models, employing the parameters given in Table 5. Figure 10 presents the pressure head profile for the three soil types and Figure 11 the computed relative root water uptake from the soil column. Note that only in the case of SWAP-macro the soils pressure head distribution has a direct relation to water uptake distribution. In the other three models the relation is indirect: in case of SWAP-micro via the pressure head at the soil-root interface (PHR), for FUSSIM2 via PHR, the root pressure head (PHX) and radial root resistance, and in RSWMS via PHR, PHX, root radial and axial resistance. The water uptake distribution of FUSSIM2 shows the largest differences between the three soils, which has to do with the fact that here in case of clay and loam hydraulic lift occurred in the upper 10-15 cm. The other models showed a similar pattern of uptake distribution for all three soils, especially in the case of RSWMS.
Total water uptake rate in cm d! of the models corresponding to the pressure head distribution given in Figure 10. Table 6
Total water uptake rate in cm d! of the models corresponding to the pressure head distribution given in Figure 10. Table 6
Simulated relative root water uptake of the four models, corresponding to the pressure head distribution depicted in Figure 10, root densities depicted in Figure 5 and potential transpiration rate 0.4 cm d!
Simulated relative root water uptake of the four models, corresponding to the pressure head distribution depicted in Figure 10, root densities depicted in Figure 5 and potential transpiration rate 0.4 cm d!
Time of onset of the reduction period and the total transpiration realized in 30 d for the different models in scenario S1. Table 7
Time of onset of the reduction period and the total transpiration realized in 30 d for the different models in scenario S1. Table 7
As Figure 13 fort = 15.5.
As Figure 13 fort = 15.5.
As Figure 13 for t = 30.5 a.
As Figure 13 for t = 30.5 a.
Differences in pressure head at root surface (PHR), in root xylem (PHX) and gradient of pressure head between root surface and xylem (PHX-PHR) between results of RSWMS and FUSSIM2.
Differences in pressure head at root surface (PHR), in root xylem (PHX) and gradient of pressure head between root surface and xylem (PHX-PHR) between results of RSWMS and FUSSIM2.
Figure 17 Relative water uptake as a function of root length density and pressure head at t = 0.5 d (left column) and t = 15 d (right column).
Figure 17 Relative water uptake as a function of root length density and pressure head at t = 0.5 d (left column) and t = 15 d (right column).
Total transpiration (cm) after 15 days in scenario S1 and S2. Table 8
Total transpiration (cm) after 15 days in scenario S1 and S2. Table 8
Time course of cumulative transpiration for S1 (left column) and 82 (right column).
Time course of cumulative transpiration for S1 (left column) and 82 (right column).
Figure 21
Figure 21
Figure 22
Figure 22
a) Pressure head distribution after 10 days for the three cases considered, and b) cumulative transpiration for the three cases considered.
a) Pressure head distribution after 10 days for the three cases considered, and b) cumulative transpiration for the three cases considered.
Relation between the conductance in the path root - leaf for maize and potential transpiration. Data of Zhuang et al. (2001). According to the study of Zhuang et al. (2001) the conductance in a maize plant in the path root - leaf is a function of the potential transpiration (Figure A-1). So the leaf water potential can be calculated as:
Relation between the conductance in the path root - leaf for maize and potential transpiration. Data of Zhuang et al. (2001). According to the study of Zhuang et al. (2001) the conductance in a maize plant in the path root - leaf is a function of the potential transpiration (Figure A-1). So the leaf water potential can be calculated as:
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Alterra is part of the international expertise organisation Wageningen UR (University & Research centre). Our mission is ‘To explore the potential of nature to improve the quality of life’. Within Wageningen UR, nine research institutes — both specialised and applied — have joined forces with Wageningen University and Van Hall Larenstein University of Applied Sciences to help answer the most important questions in the domain of healthy food and living environment. With approximately 40 locations (in the Netherlands, Brazil and China), 6,500 members of staff and 10,000 students Wageningen UR is one of the leading organisations in its domain worldwide. The integral approach to problems and the cooperation between the exact sciences and the technological and social disciplines are at the heart of the Wageningen Approach.

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Experimental results obtained from a greenhouse trial with common bean (Phaseolus vulgaris L.) plants performed to test model hypotheses regarding the onset of limiting hydraulic conditions and the shape of the transpiration reduction curve in the falling rate phase are presented. According to these hypotheses based on simulations with an upscaled single-root model, the matric flux potential at the onset of limiting hydraulic conditions is as a function of root length density and potential transpiration rate, while the relative transpiration in the falling rate phase equals the relative matric flux potential. Transpiration of bean plants in water stressed pots with four different soils was determined daily by weighing and compared to values obtained from non-stressed pots. This procedure allowed determining the onset of the falling rate phase and corresponding soil hydraulic conditions. At the onset of the falling rate phase, the value of matric flux potential M l showed to differ in order of magnitude from the model predicted value for three out of four soils. This difference between model and experiment can be explained by the heterogeneity of the root distribution which is not considered by the model. An empirical factor to deal with this heterogeneity should be included in the model to improve predictions. Comparing the predictions of relative transpiration in the falling rate phase using a linear shape with water content, pressure head or matric flux potential, the matric flux potential based reduction function, in agreement with the hypothesis, showed the best performance, while the pressure head based equation resulted in the highest deviations between observed and predicted values of relative transpiration rates.

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Root water uptake as simulated by three water flow models (Online first
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We compared four root water uptake (RWU) models of diff erent complexity that are all embedded in greater soil water fl ow models. The soil models used were SWAP (one-dimensional), FUSSIM2 (two-dimensional), and RSWMS (three-dimensional). Within SWAP, two RWU func ons were u lized (SWAP-macro and SWAP-micro). The complexity of the processes considered in RWU increases from SWAP-macro, to SWAP-micro, to FUSSIM2, to RSWMS. The objec ve of our study was to determine to what extent the RWU models diff ered when tested under extreme condi ons: low root length density, high transpira on rate, and low water content. Comparison 1 looked at the results of the models for a scenario of transpira on and uptake and Comparison 2 studied compensa on mechanisms of water uptake. The uptake scenario pertained to a long dry period with constant transpiraon and a single rainfall event. As could be expected, the models yielded diff erent results in Comparison 1, but the diff erences in cumula ve transpira on were modest due to various feedback mechanisms. In Comparison 2, the cumula ve eff ect of diff erent feedback processes were studied. Redistribu on of water due to soil pressure head gradients generated by water uptake led to an increase in cumula ve transpira on of 32%, and the inclusion of compensa on in uptake by the roots resulted in a further increase of 10%. Going from one-to three-dimensional modeling, the horizontal gradients in the soil and root system increased, which reduced the actual transpira on. The analysis showed that both soil physical and root physiological factors are important for proper determinis c modeling of RWU.

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Determination of empirical parameters for root water uptake models
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