How much water can be taken up by roots and how this depends on the root and water distributions in the root zone are important questions that need to be answered to describe water fluxes in the soil–plant–atmosphere system. Physically based root water uptake (RWU) models that relate RWU to transpiration, root density, and water potential distributions have been developed but used or tested far less. This study aims at evaluating the simulated RWU of winter wheat using the empirical Feddes–Jarvis (FJ) model and the physically based Couvreur (C) model for different soil water conditions and soil textures compared to sap flow measurements. Soil water content (SWC), water potential, and root development were monitored noninvasively at six soil depths in two rhizotron facilities that were constructed in two soil textures: stony vs. silty, with each of three water treatments: sheltered, rainfed, and irrigated. Soil and root parameters of the two models were derived from inverse modeling and simulated RWU was compared with sap flow measurements for validation. The different soil types and water treatments resulted in different crop biomass, root densities, and root distributions with depth. The two models simulated the lowest RWU in the sheltered plot of the stony soil where RWU was also lower than the potential RWU. In the silty soil, simulated RWU was equal to the potential uptake for all treatments. The variation of simulated RWU among the different plots agreed well with measured sap flow but the C model predicted the ratios of the transpiration fluxes in the two soil types slightly better than the FJ model. The root hydraulic parameters of the C model could be constrained by the field data but not the water stress parameters of the FJ model. This was attributed to differences in root densities between the different soils and treatments which are accounted for by the C model, whereas the FJ model only considers normalized root densities. The impact of differences in root density on RWU could be accounted for directly by the physically based RWU model but not by empirical models that use normalized root density functions.
Root water uptake (RWU) is a vital process for plant functioning since it conditions nutrient transport and balances transpiration. Estimations of RWU are needed to make predictions of crop water use, to assess water and nutrient use efficiency as a function of root architecture and environmental controls, and to design efficient water and nutrient resource management in agricultural practices (Molz, 1981). However, quantifying RWU for water and nutrient management in different regions and climates continues to be a challenge due to the lack of knowledge of key RWU parameters and appropriate description of the RWU process (Vereecken et al., 2016). Typically, RWU is estimated from the transpiration demand, which is calculated from the canopy energy balance under the assumption that the crop is well watered. Different soil water balance models have been developed that allow RWU to be estimated using different parameterizations of the root system and water uptake mechanisms. However, the availability of field-plot-scale experiments in different soil textures and for different soil water regimes that are needed to validate and improve these models is very limited.
In many soil water balance models that are used to predict RWU, the Richards equation is used for calculating water flow in
unsaturated soils and a sink term is defined that describes RWU:
Besides transpirational demand and soil water pressure head (SWP), RWU is also influenced by root hydraulic properties (i.e., root hydraulic conductance) which may vary over time due to root development and growth (Doussan et al., 1998; Steudle, 2000; Javaux et al., 2008). Root hydraulic properties determine the resistance to water flow within the plant and define the water potential losses along the sap flow from the roots to the shoot and the leaves (Bechmann et al., 2014). The relation between soil water and leaf water potentials and sap flow depends on root hydraulic properties, which therefore should be considered in RWU models (Vereecken et al., 2015; Vadez, 2014). Physically based macroscopic RWU models were developed that describe water fluxes in the soil–root (or soil–root–plant) system based on water potentials and conductivities or conductances of the soil and the root system. Nimah and Hanks (1973) characterized water uptake as a function of root density, axial root conductance, and water potential at the root collar. Heinen (2001) considered root hydraulic properties and water pressure head at the root–soil interface in the RWU model but without considering water uptake compensation. Van Lier et al. (2008) developed a 1-D water flow model in which the RWU rate was a function of root surface water potential and root radius. This model considered implicitly lateral flow from the soil to the root with an implicit compensation mechanism but did not include the information about axial root hydraulic conductances.
In order to present a mechanistic description of the RWU process that contains physically defined parameters, Couvreur
et al. (2012) developed a 3-D model based on the approach of root system hydraulic architecture (Doussan et al., 2006;
Javaux et al., 2008). In this model, RWU is dependent on root system hydraulic conductance (
Another way to validate the inversely estimated parameters is to evaluate whether the model is able to predict the RWU and its reduction when SWP decreases. For crops with a small water capacity, the RWU corresponds closely with the transpiration rate. Measurements of crop transpiration can therefore be used to parameterize or validate RWU models.
Many techniques have been used to investigate transpiration ranging between the single plant and catchment scale (Twine
et al., 2000; Allen et al., 1989; Jaeger and Kessler, 1997). At the field plot scale, weighing lysimeters allow
transpiration to be measured (e.g., Groh et al., 2016; Garré et al., 2011). A disadvantage of lysimeters is that they are costly and,
although possible (e.g., Garré et al., 2011; Vandoorne et al., 2012), root distributions are difficult to measure in
lysimeters and their spatial growth is influenced by the confined soil space, which also frequently causes undesired
boundary effects (e.g., high root length densities at lysimeter walls). Measuring sap flow with the thermoelectric method
is a direct and in situ technique which was discovered by Huber (1932). It was used to estimate transpiration for
different trees species (Granier et al., 1996; Cermak et al., 2004; Massai and Remorini, 2000) and crops (Chabot et al.,
2005; Langensiepen et al., 2014; Cohen et al., 1993). Due to limitations of sensor installation on small and vulnerable
crop stems, sap flow measurements on crops with small stem diameters of less than 5
The main objective of this study is to investigate whether physically based (1-D Couvreur model) and empirical (Feddes–Jarvis model) models for RWU can simulate the effect of different soil water availability levels on wheat RWU resulting from differences in soil water application and differences in soil water retention characteristics. This includes testing whether parameters of these models can be calibrated using measurements of soil water content, water potential, and root density and validating the calibrated model against sap flow measurements. Second, we investigated whether differences in crop shoot and root developments between treatments with differences in soil water availability lead to different model parameter estimates and whether these parameters estimates can be linked to directly observable properties of the root system.
Therefore, water potentials and contents, root distributions, crop development, and sap flow were monitored in six plots (two soil types and three water application treatments) and used to parameterize two RWU models: the Feddes–Jarvis model (FJ model) and the physically based Couvreur model (C model).
The experimental setup of the plots was described in detail in Cai et al. (2016) and the model setup and the inverse modeling procedure that was used to determine the parameters by Cai et al. (2017). For more detailed information about the setup and the inverse modeling procedure, we refer the reader to these publications.
Sketch map of the location and the setup of the upper (F1, stony soil) and lower (F2, silty soil) rhizotron facilities. P1, P2, and P3: the sheltered, rainfed, and irrigated plots.
Two instrumented rhizotron facilities were constructed on the upslope and the downslope of a cropped field in Selhausen
(Germany, 50
Precipitation and other meteorological data for the calculation of reference evapotranspiration (
Winter wheat (variety Ambello) was sown at a density of 300–320
Time domain reflectometer (TDR) sensors, tensiometers (T4e, UMS GmbH, München, Germany), and matrix water potential sensors
(MPS-2, Decagon Devices Inc., UMS GmbH München, Germany) were installed in each plot at 0.1, 0.2, 0.4, 0.6, 0.8, and
1.2
Root distributions were measured nondestructively at weekly intervals from 11 February to 11 July 2014 in the stony soil
and from 14 March to 24 July 2014 in the silty soil with a minirhizotron camera (Bartz Technology Corporation,
Carpinteria, CA, USA) in 7 m long horizontally installed rhizotubes. Three replicates of rhizotubes were installed at the
same depths as the soil moisture sensors. Root images with the size of 16.5
Sap flow was determined with SGA3 Dynagage sap flow sensors (Dynamax Inc., Houston, USA) in five randomly selected wheat
tillers located in the center of each plot. They were continuously operated from 23 May to 6 July 2014. Signals of
the sap flow sensors were scanned every 60 s with Dynamax control units consisting of voltage regulators, AM 16/32B
multiplexers, and CR1000 data loggers (Dynamax Inc., Houston, USA; Campbell Scientific, Logan, Utah). The readings were
averaged every 10 min, stored in a text file and processed with an R script containing the standard calculation
procedures for computing sap flow from Dynagage files (Dynamax, 2009) and an improved post-processing method for removing the noise from standard calculations (Langensiepen
et al., 2014). Tiller density was determined in a fixed area of 1
We used two 1-D RWU models: the FJ model (Šimůnek and Hopmans, 2009) and the physically based C model (Couvreur
et al., 2012, 2014a), both of which considered water uptake compensation. The two models have been implemented in
Hydrus-1-D (Šimůnek et al., 2016). The sink term in the two models is calculated with the following equations:
Crop coefficients (
When the total resistance to flow in the axial direction is small (large
axial conductance and/or small transport
distance), then the 3-D version of the C model reproduces the flow in the root system exactly that is
predicted by solving the flow equations in the root system for boundary conditions that correspond with the soil water
potentials (Couvreur et al., 2014b, 2012). In these conditions,
The parameters
For the FJ model, the RWU under water stress conditions was constrained by a piecewise function (
The water uptake compensation in the C model is described by the second term on the right-hand side of
Eq. (
The soil hydraulic properties were described by the combined Mualem–van Genuchten equations (Mualem, 1976; Van Genuchten,
1980):
Parameters of soil hydraulic properties in the topsoil (0–30
The parameters of the van Genuchten (1980) soil water retention function were fitted using measured SWC and soil water
head data (Cai et al., 2016) (Table 2). The parameters
The 1-D Richards equation was solved numerically using Hydrus in a 145
The model results were evaluated in terms of root mean square error (RMSE), mean bias error (ME), and an index of
agreement (
We first discuss the effect of water treatments and soil textures on crop and root development. In the second part, we discuss the inverse estimation of RWU parameters of the FJ and C models from measured SWC and SWP. In the third part, simulated RWU by the two models in the different soils and water treatments is discussed and compared with sap flow measurements. In the last part, we discuss a sensitivity analysis that was carried out to evaluate the effect of the differing development of the wheat crop in the different soils and water treatments on the simulated water uptake.
Tiller density (measured on 11 Jun 2014), crop biomass (including straw and grain, which were measured after the harvest), ratio of leaf area index (LAI) to tiller density, and maximal root length in the three plots (P1: sheltered; P2: rainfed; P3: irrigated) of the stony (F1) and silty (F2) soils.
Tiller densities and crop biomass in the three different water treatments in the two soils are shown in Table 3. Contrasting soil water availability affected crop biomass growth and yield. Less water application (the sheltered plot received 55.13 and 44.52 % of the water received by the irrigated plots in the stony and silty soil, respectively; Fig. 2b) reduced the tiller density in the sheltered plot with respect to the irrigated plot by 38.4 % in the stony plots and 11.3 % in the silty plots, and reduced the biomass by 58.8 % in the stony plots and 40.8 % in the silty plots. The biomass of wheat in the treatments that received less water was reduced more strongly than the tiller density as was also reported by Musick and Dusek (1980). The tiller density and biomass were generally higher in the silty soil than in stony soil, especially for the sheltered plots. Similar differences were found in LAI between the two soils (Fig. 2a). The peak LAI was higher in each plot of the silty soil than the corresponding plot of the stony soil. The higher water-holding capacity of the silty soil supplying more available water in the subsoil for root extraction may account for the difference. Note that there was no difference of LAI among all the plots of the two soils until the beginning of April. The deviation of LAI between the plots with different water treatments started around 50 days earlier in the stony than in the silty soil even though the irrigation was applied earlier in the stony plot. This indicated that more water was available in the silty soil than in the stony soil due to the different soil properties.
Depth–time distribution of root length density (RLD) in the three plots (P1: sheltered; P2: rainfed; P3: irrigated) of
As for the belowground part of the crops, RLD decreased gradually downwards for all plots of the two facilities at the
beginning of the measurements (Fig. 3). The RLD in the shallow layers (
Root senescence was observed at the end of the growing season. It started in the upper soil layers and progressively moved
to deeper layers, which is more obvious in the three plots of the stony soil after 21 May. Furthermore, root senescence in
shallower layers (above 30
Ratio of total root length to biomass in the three plots (P1: sheltered; P2: rainfed; P3: irrigated) of the stony (F1) and silty (F2) soils.
The observed root development in the two different soils and for the different water treatments show opposite reactions to soil water availability. On the one hand, lower water availability in the stony soil led to a lower root density and lower total root length than in the silty soil (Table 3). The same behavior was observed when comparing the sheltered with the rainfed and irrigated plots in the stony soil. In the silty soil, however, an increase in root density was observed when water availability decreased. When plants experience water deficits, the aboveground shoot development is reduced by different mechanisms (e.g., reduced leaf expansion by lower turgor, enhanced respiration, stomatal closure, and reduced photosynthesis) (Bunce, 1978; Wesselius and Brouwer, 1972; Mansfield and Atkinson, 1990). The reduction in shoot growth can be counteracted with an increase in carbon allocation to the root zone as was shown in a review by Poorter et al. (2012) on environmental effects on biomass allocation. The ratio of total root length to aboveground biomass (Fig. 4) suggests that indeed a larger fraction of carbon was allocated to the roots in the sheltered plots than in the rainfed or irrigated plots both in the stony and silty soils. Although the differences in the ratio between the two soils are not so large, the total root length per kilogram of shoot biomass was larger in the silty soil than in the stony soil. At first sight, this seems contradictory to the lower water (and nutrient) availability in the stony soil than in the silty soil. This might reflect the fact that other factors like soil mechanical strength may have restricted root growth more in the stony soil than in the silty soil (Unger and Kaspar, 1994; Merotto Jr and Mundstock, 1999).
Comparison between observed (black) and simulated
Same as Fig. 5 but for silty soil from 22 May to 30 July 2014.
Time series of observed and simulated SWC and SWP are illustrated in Figs. 5 and 6 for the plots with different water
treatments of the stony and silty soils, respectively. As expected, the irrigated plots were wetter than the rainfed and
sheltered plots but in the top layers of the silty soil measured water contents and pressure heads decreased between
irrigation events to similarly low values as in the nonirrigated plots. For the period in which measurements were carried out
in both soils (from the middle of May until the beginning of July) the SWPs in the sheltered and rainfed plots were more negative in
the stony than in the silty soil, suggesting that the crop experienced more water stress in the stony soil. In both soils,
the top layer dried out considerably and low SWP (
The statistics RMSE, ME, and
The saturated hydraulic conductivity (
The obtained soil hydraulic parameters, parameters of the water stress function of the FJ model, and root system
parameters of the C model are listed in Table 4. The corresponding hydraulic conductivity curves are plotted in Fig. S1 in
the Supplement. For the stony soil, the soil hydraulic parameters estimated by the two models were comparable but larger
differences between the model parameters were obtained for the subsoil layer of the silty soil. Smaller (even negative)
tortuosity parameters
For the FJ model, parameters of the stress function were similar for the stony and silty plots, which implies that the
estimated parameters were not sensitive to the different root densities in the two different soils. It is important to note
that the difference in root density between the different water treatments in one soil was not considered in the model
since only one parameter set was used to simulate the different water treatments. The obtained threshold values of the
stress function
The values of
Estimated root hydraulic conductance (
Temporal changes in root system hydraulic conductance
Response surface for
To evaluate the uniqueness of the estimated parameters of the FJ and C models, response surfaces of the objective function
were plotted. Selected contour plots in Fig. 8 show that the soil hydraulic parameters were identifiable. The parameters
in the C model were also identifiable in both soils but
In contrast to the current study, Cai et al. (2017) inversely estimated the soil hydraulic parameters and parameters of
the FJ and C models using only observations from the sheltered plot in the stony soil. Inclusion of data from the rainfed
and irrigated plots had an impact on the optimized soil hydraulic parameters (see values in parentheses in
Table 4),
whereas similar values of the root hydraulic conductances
Potential evapotranspiration (
The cumulative
Daily cumulative potential transpiration (
Correlation between sap flow (SF) and root water uptake (RWU) simulated by the Feddes–Jarvis (FJ) and Couvreur (C) models of the stony (F1) and silty (F2) soils. The crosses (x) obtained by the FJ and C models overlapped in F2.
Figure 10 shows potential and actual RWU simulated by the FJ and C models and sap flow in the three plots of the stony
soil and the silty soil from 23 May to 6 July 2014. When the measured sap flow was regressed against the simulated RWU by
the two models, there was a good agreement between crop transpiration obtained from the sap flow measurements and model
simulations with
There was, as far as we know, no similar comparison between sap flow and simulated RWU using field observations for wheat crop. Due to the “delicate anatomy of the walls of hollow wheat stems” (Langensiepen et al., 2014), it is challenging to install the sensors and measure the temperature variation of the thin wheat stalk with high time frequency for the field condition. Furthermore, spatial variation in environmental conditions that influence the sap flow in a single stem and variability in stem development lead to a considerable stem to stem variability in sap flow in which the average deviation from mean sap flow is quantified for the three different treatments shown in Fig. 10 (Chabot et al., 2005; Zhang et al., 2014). The simulated RWU was based on a chain of models linked with assumptions and preset parameterizations starting from the calculation of the potential crop evapotranspiration using the empirical FAO56 approach, its split into soil evaporation and transpiration as a function of LAI, and its reduction to actual transpiration as a function of soil water potential. The overall good correlation between simulated RWU and sap flow measured transpiration therefore gives some confidence in the used approaches.
Relation between the ratio of the RWU in the stony soil to the RWU in the silty soil estimated by the FJ and C models in the three plots (P1: sheltered; P2: rainfed; P3: irrigated) and the ratio of sap flow in the stony soil (F1) to that in the silty soil (F2).
In order to unravel the model's capability to calculate RWU in different soils and for different water treatments further,
we made plots of the ratios of the measured sap flow in the two soils vs. the ratios of simulated RWU in the two soils for
the different water treatments (Fig. 12). Ratios were used to cancel out the temporal variations due to varying
meteorological conditions. The good agreement between measured and simulated ratios for the irrigated plots, in which RWU
was not influenced by water availability, indicates that the differences in potential transpiration rates between the two
plots due to different crop development (ripening) and LAI were adequately represented in the models. There is no
difference between the FJ and C models since RWU is completely defined as a boundary condition and is not dependent on the
soil water status in the irrigated plots, which was discussed by Cai et al. (2017). For the rainfed and sheltered plots,
the correlation between the measured and simulated ratios is smaller. These ratios represent to what extent the simulated
reduction of RWU in the stony soil due to reduced water availability is consistent with the measured reduction in sap flow
relative to the simulated RWU and measured sap flow in the silty plots where there was no reduction in RWU. Of note is
that simulations by the C model are more consistent with the sap flow measurements than the simulations by the
FJ model. The ratios of the FJ model simulations vary less than the ratios of the sap flow measurements, whereas the range
of ratios of the C model simulations is more in agreement with the sap flow measurements. This indicates that the C model
represents how changing soil moisture and soil moisture distributions change the
RWU better than the FJ model. Furthermore, since the root hydraulic conductance in the C model depends on the root density, the model can reflect
the impact of the differences in root density between the different water treatments on RWU. The FJ model did not possess
this flexibility since only one set of water stress parameters was used for the different water treatments. Similar
observations were made by Vandoorne et al. (2012) who optimized the water stress parameters of the FJ model for chicory
(
Sap flow per unit soil surface area was obtained by multiplying the average sap flow in the measured tillers by the number of tillers per unit soil surface area. Figure 13 shows the average sap flow per tiller and the sap flow per unit leaf area index. For the silty soil, the sap flow per tiller and sap flow per leaf area were very similar for the different water treatments. For the stony soil, the sap flow per tiller in the irrigated plot was similar to that in the silty soil until approximately 15 June. After that, the sap flow per tiller reduced in the irrigated plot of the stony soil because of the reduction in leaf area (the sap flow per leaf area remained similar to that in the silty soil). Water stress limited the leaf development of wheat in both longevity and quantity (Khalid et al., 2016; Zhou et al., 2015). The sap flow per tiller in the rainfed plot of the stony soil became smaller than that in the irrigated plot or in the silty soil after 11 June but recovered for a short time period to the same sap flow after the rainfall on 10 June. This recovery was also observed for the sap flow in the sheltered plot of the stony soil. However, the sap flow per tiller was generally lower in this plot than in the other plots. This indicates that transpiration in this plot was reduced by both a reduced number of tillers and a lower flux per tiller. It is interesting to note that the sap flow per leaf area surface in the sheltered stony plot shortly increased to higher values than in other plots after the rainfall event on 10 June.
Cumulative root water uptake simulated by the Couvreur model using root hydraulic conductance (
The different root development in the two soils and for the different water treatments (Fig. 3) was related to a different
parameterization of the root hydraulic conductance (Fig. 7). The different shoot development and different LAI values
(Fig. 2a) affected calculations of potential transpiration rates (Fig. 9) that were used as boundary conditions for RWU
simulations. In order to demonstrate the impact of the plant development on the RWU simulation, we conducted two sets of
simulations in which the plant parameters were prescribed by measurements done in another soil and/or water treatment. In
the first set of simulations, we changed the root hydraulic conductance,
In a second set of simulations, we changed the calculated potential transpiration of the sheltered stony plot to that of
the irrigated stony plot (Fig. 14). Only the stony soil was considered since the shoot and LAI development did not differ
considerably between the different water treatments in the silty plot. Until 1 May, there was almost no difference in the
LAI and
Measured sap flow (SF) per tiller
Of interest is also the time at which water uptake starts to decrease and its effect on plant development. In the sheltered and rainfed stony plots, a slight reduction in RWU is simulated during April. This reduction in RWU was accompanied by only a slight decrease in LAI development compared to the irrigated plot (Fig. 2a). After the middle of May, which is also the period when RWU reduced more strongly, the LAI did not increase anymore in the sheltered plots, whereas in the other plots of the stony soil, it reached its maximum at the beginning of June. In the silty soil, the maximum was reached at the beginning of July. The root system reached its full development, however, earlier than the time when the LAI reached its maximum (Fig. 3). The root system development in the stony plot was much more strongly reduced by the lower water availability in April than the LAI development. Both leaves and roots showed reactions to environmental changes but these reactions were not simultaneous. Walter and Schurr (2005) reviewed studies of leaf and root growth of herbaceous plants and indicated that roots experienced the effect of environmental factors (i.e., water stress, nutrient deficiency) more directly compared with leaves. They also indicated that roots responded faster than leaves to the environmental conditions to optimize resource use efficiency.
The different crop development of winter wheat had consequences for the parameterization of RWU models. First, the
different shoot development led to differences in boundary conditions such as the potential evapotranspiration
(
Daily potential (
The C model, which is based on a physical description of the flow in the soil–root system, represented the effect of the differences in root system development on RWU directly since we related the root system conductance to the root length. When root parameters that were obtained from the sheltered stony plot were used to predict RWU in the silty soil, water stress was simulated in the silty soil. On the other hand, when root parameters obtained from the silty soil were used to simulate water uptake in the stony plot, the water uptake could only slightly be increased but the “severity” of the water stress remained the same. This suggests that the root system that developed in the stony soil would be under-dimensioned for the silty soil and the opposite for the root system that developed in the silty soil. It also suggests that considering the link between root conductance and total root length gave the model extra flexibility to describe root water uptake for different scenarios of root water availability (both due to different soil types and water treatments). Therefore, when using the C model, in addition to the information about rooting depth and relative root density distributions, information about the total root length is also directly used to describe the temporal evolution of the root system conductance in different soils and for different water treatments.
The simulated differences in transpiration from the two different soils and the different water treatments could be
confirmed by sap flow measurements. The physically based C model predicted the ratios of the transpiration fluxes in the
two soil types slightly better than the FJ model. Since the transpiration from the silty soil was close to
This study illustrated that a combined dataset of root and shoot development, of soil water contents and soil water potentials, and of transpiration fluxes derived from sap flow measurements can be used to parameterize and validate RWU models. These models require inputs from root and shoot developments, which were observed to depend strongly on the environmental conditions. How far the C model can improve prediction of RWU, transpiration, and soil water stock depletion in widely used crop models for different crops and climate conditions is the subject of further investigations. Next to improving the description of the RWU, the C model also simulates the water potential in the root collar. In the current model formulation, the water potential in the collar is used as a control variable which is kept fixed when a critical threshold value is reached. We interpreted the reduction in transpiration when this threshold was reached as water stress. However, we observed considerable reduction in aboveground biomass even when no reduction in transpiration was simulated (or observed with sap flow measurements), e.g., in the sheltered and rainfed silty soil plots. Next to transpiration, stomatal opening, and carbon assimilation, plant growth is also linked to the hydraulic status of the shoot (Tardieu et al., 2014). Predictions of the shoot water potential, which is closely linked to the water potential in the root collar, using models that simulate water fluxes in the soil–plant–atmosphere system, provide information for growth models that simulate the reaction of plant growth to environmental conditions related to drought stress. Therefore, linking growth and water flux models is important for understanding and predicting the interactions between plant growth and soil water availability.
Concerning the observations of the root development using horizontally rhizotubes, it needs to be further investigated how root counts along rhizotubes can be translated to root densities. Also, the reasons for the constant offset between the simulated transpiration and the sap flow measurements need to be investigated further.
The meteorological data that were obtained from a climate station located in Selhausen
(Germany) are freely available on the TERENO data portal (
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
This study was financially supported by SFB/TR 32 (Transregional Collaborative Research Centre 32, funded by the Deutsche Forschungsgemeinschaft (DFG)). The meteorological data were obtained from the online database of the project TERENO. The rhizotron facility is part of the TERENO network of terrestrial observatories. The authors thank the reviewers for their valuable comments and suggestions to improve the manuscript. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Nunzio Romano Reviewed by: two anonymous referees