To observe the temporal dynamics of water within the soil–plant–atmosphere continuum (SPAC), isotopic labeling experiments offer a unique opportunity to create distinct pulses that can be traced from the soil, through the plant, to the atmosphere. For small experimental plots, chamber-based measurements can capture the isotopic composition of transpiration (δT) following isotopically labeled irrigation pulses (e.g., ). Due to dimensional limits set by the size of the required chamber, this method is not applicable to adult trees.

Larger-scale irrigation experiments were conducted in green house experiments with around 15 m high tropical trees and in a central European forest with grown, 25 m high, specimens of Fagus sylvatica and Abies alba . Instead of chamber measurements of δT, they extracted water from tree crown branches to monitor the isotopic composition of xylem water (δxyl). For 7 months, had a weekly δxyl sampling scheme, while started with a sub-daily δxyl sampling scheme for 5 d and continued the following 2 months with a sampling frequency of 4 to 6 d. Both experiments observed notable delays (days to weeks) between tracer application and detection within the sampled crown branches.

A more specific investigation of tree water dynamics can be achieved by skipping soil and roots and directly injecting small amounts of D2O into the stem base . Due to the high deuterium concentrations of the injected label, tracer breakthrough curves within the tree crown could be acquired by analyzing condensate from branch or foliar samples placed into zipper bags. Time delays between tracer application and maximum tracer concentrations within the tree crowns have mostly been reported to amount to a few days, but for a 50 m high specimen of Tsuga heterophylla also reported a delay of about 30 d. A comparison of heat-tracing-derived sap flux velocities with isotope-tracing-derived velocities revealed that the latter may be 4 to 16 times higher .

have reviewed 159 studies combining root water uptake (RWU) and isotopes. A total of 46 % of those studies used isotopic data to infer a specific soil layer or water pool as a source of RWU. Another 50 % of those studies used two- or multi-source linear mixing models of varying statistical sophistication. Only the remaining 4 % of the reviewed studies used physically based analytical or numerical models. This means that the vast majority of isotope-based RWU studies are based on graphic or statistical methods, which allow a description of observations but abstain from offering physically based models, which could be used to predict the reaction of RWU to changing environmental conditions.

, and have modeled RWU of trees with implementations of a Feddes-style RWU model described by and as implemented within the soil hydrological model HYDRUS-1D . Even though the Feddes RWU model was originally developed to model water uptake of agricultural crops, the above-listed applications demonstrated that Feddes RWU models are also suited to simulate RWU of mature trees. used a Feddes RWU model, driven with soil water potentials and soil 18O concentrations simulated with an isotope-enabled version of HYDRUS-1D , to compute δ18O signatures of RWU. These predictions compared well to fortnightly sampled δ18O values of branch xylem water.

The assumption that isotopic signatures of RWU (δRWU) are directly related to simultaneously sampled δxyl has been challenged by studies of and . juxtaposed a “zero storage case” (δRWU=δxyl) and two alternative cases (well mixed and piston flow) that included tree internal water storage. Model results for the cases with tree internal water storage compared better to observational data than the zero storage case. Due to a limited temporal resolution of their observed data, were not able to conclude whether the piston flow or the well-mixed case was more appropriate and hypothesized that the actual behavior of the system may lie between those two cases. proposed a model that comprised a soil-water-potential-driven RWU component and a stem water transport module that is based on an advection–diffusion model coupled to sap flow velocities. Based on their model, predicted that diel fluctuations of δRWU (caused by fluctuations in leaf water potential) should be transmitted from the stem base upwards, effectively causing periodic patterns of δxyl along the stem height.

Until recently, measurements of δxyl and isotopic compositions of soil water (δsoil) usually required the laborious extraction of the respective waters. Scholander pressure chambers can be used to extract xylem water from branches . Another common xylem water extraction method is cryogenic vacuum extraction , which is also commonly used for soil pore water extraction . A detailed review on available soil pore water extraction techniques was done by . All of these methods require destructive sampling of plant or soil material and subsequently careful sample storage and treatment. The required effort per sample and the disturbance caused by each sampling limit the total number of samples as well as the maximum sampling frequency. In fact, the very nature of destructive sampling renders repeated measurements from the exact same spot impossible. Consequently, a time series generated with a destructive sampling method will inevitably also be affected by spatial variability.

With the advent of laser spectroscopy, the measurement of stable water isotopes does require the extraction of liquid water samples not any longer. Instead, the isotopic composition of the vapor contained in a gaseous sample can directly be analyzed in the lab and even in the field. Firstly, this leads to the development of equilibration-based lab methods which allow for indirect water isotope measurements from samples without the need for the extraction of liquid water from destructive samples . Subsequently, different approaches for in situ sampling of stable water isotopes have been developed. For a thorough review of in situ water isotope sampling techniques we would like to refer to .

Different approaches for in situ measurements of δsoil have been proposed and tested by and . So far the method of has seen the most subsequent applications ranging from long-term, continuous lab experiments to campaign-based field studies . For in situ sampling of δxyl, developed the borehole equilibration method, which goes entirely without a specific probe and instead connects tubing directly to a borehole through a stem. So far, this method only has been tested on cut trees that drew water up through their stems under tension derived from transpiration and in a greenhouse experiment with small trees placed in pots filled with water instead of soil.

The in situ probes developed by are the only approach that has been proven to work in soil (in six 2 d sampling periods; ) as well as within tree xylem (in two young Maple trees over 11 d; ). While these probes have been called SWIPs (soil water isotope probes) when used in the soil and XWIPs (xylem water isotope probes) when used in tree xylem, the actual probes in our study are identical in both use cases. Therefore we propose an alternative third name: WIP (water isotope probe), which should encompass both of the mentioned and all further use cases of this particular probe design.

From the raw sensor data, we computed the sap flow velocity vsap in ms-1 according to : 16vsap=2kCw(ru+rd)ln⁡ΔTuΔTd, where k is the thermal conductivity of sapwood set to 0.5 Wm-1K-1 , Cw is the specific heat capacity of water at 4.184×106 m3K-1, ru and rd (both = 6 mm) are the distances of the central heater needle to the up- and downstream thermistor needles, and ΔTu and ΔTd refer to the temperature changes induced by the heating pulse at the up- and downstream needles, respectively.

Our measured sap flow time series was limited from May 2019 to 8 August 2019. In order to extend it to the whole year, we assumed no sap flow during the time where our deciduous trees did not have any foliage (before May and after October). During those periods, we set vsap to 0 ms-1. For the remaining period between 8 August and 31 October, we fitted the two parameters a and b of the following equation: 17vsap=VPD×a/(VPD+b), where VPD is the vapor pressure deficit (derived from meteorological data of the nearby meteorological site Klippeneck of the German Weather service DWD). In order to account for decreasing vsap due to leaf senescence, we multiplied the estimates obtained by Eq. () with a linearly decreasing reduction factor between the middle of September and end of October. reported a comparable autumnal reduction of sap flow in relation to potential evaporation for central European beech trees.

As an additional means to investigate RWU independently of isotope measurements, we followed and used measurements of volumetric soil moisture (averaged across the four available depth profiles) – more specifically the daily decline of soil moisture during dry days – as an indicator of RWU. To compare the soil moisture measurements with the RWU model, we derived a water uptake ratio rRWU in two ways: 18rRWU=ΔθuΔθl=S‾uS‾l, where the first ratio defines the measured daily decline of soil moisture in the upper soil layer Δθu (average of 10 and 20 cm depth) and Δθl the equivalent for the lower soil layer (average 40 and 60 cm depth). The second ratio defines the relative modeled uptake strengths of Eq. () (with S‾u as the average of S‾i for the depths of 10 and 20 cm and S‾l as the average of S‾i for the depths of 40 and 60 cm). The soil-moisture-based computation of rRWU is limited to days where the soil water content throughout the depth profile is below field capacity.

In order to analyze the WIP measurements, we used the recorded valve switching times to aggregate the raw CRDS log file data by computing average values for the last 2 min of each period. The parameters of interest were sample water vapor content, δ18O and δD. In the next step we corrected for the influence of temperature on the fractionation factors during vapor equilibration at the probe head. Instead of direct temperature measurements, we relied on the assumption that the temperature at the place of equilibration (i.e., around the probe head) is reflected by the water vapor content of the obtained sample gas – given that the sample rate and the dilution rate are held constant. By computing linear regressions between measured vapor isotope values (δm) for our two standards and the sample gas moisture contents (Cm), we derived the slopes needed to correct all vapor isotope measurements to one reference moisture content value (Cr=18000ppmV) according to the following equation: 19δv=δm-ΔCδ(Cr-Cm), where δv is the corrected isotope value and ΔCδ is the slope obtained by the linear regression between Cm and δm values of the standards.

To infer the isotopic signature of the liquid water that equilibriated with the sampled vapor, we used the relationship between the known liquid phase values of our two standards and the respective observed vapor values: 20δl.x=δv.x-δv.LΔLH+δl.L, where δl.x is the normalized liquid phase isotopic value of measurement x, δv.x is the moisture-corrected vapor value of measurement x, δv.L is the moisture corrected vapor value of the light standard, δl.L, is the liquid phase isotopic value of the light standard and ΔLH is the slope obtained by 21ΔLH=δv.L-δv.Hδl.L-δl.H, with δv.H as the moisture corrected vapor value of the heavy standard and finally δl.L and δl.H as the known liquid water isotope values of the light and heavy standards, respectively.

Under stable environmental conditions, δv.L and δv.H should not change at all, but in a field experiment more frequent measurements of these standards are highly recommended. We treated both standards as regular parts of our measurement sequence, yielding one measurement of each standard every 3 to 4 h. For the normalization procedure we interpolated between those actually measured standard values in order to estimate the standard values for each measurement.

The temporal dynamics of daily sap flow velocities and soil moisture (averaged across the two profiles on the irrigated plot) are depicted in Fig. a and b. Averaged for each month, the mean daily sap flow velocities varied between 42, 88, 94 and 85 cmd-1 for May (starting at 21 May), June, July and August (ending at 8 August), respectively.

The sprinkling experiment started on 22 May during a wet period with soil moisture around field capacity (ca. 30 Vol.%). From 1 to 10 June, the first dry period occurred, with soil moisture in the topsoil decreasing towards 15 Vol.%. Several rain events between 10 and 15 June rewetted the soil, but afterwards the soil moisture in all depths declined considerably. One rainfall event with 29 mm on 12 July caused a brief rewetting of the topsoil, and a heavy convective event with 52 mm on 27 July bypassed the upper two soil moisture probes and caused a strong increase by around 10 Vol.% at 40 and 60 cm depth.

The fitted Eq. () established a solid relationship (R2 of 0.85) between vsap and VPD (see Fig. a). Since there are no systematic discrepancies between measured and VPD-derived vsap values (see Fig. a), we have high confidence in assuming that the observed periods of reduced vsap during June and July (see Fig. a) can be attributed to temporarily lowered VPD instead of soil water deficits.

In each measurement sequence 15 probes (two standards, six SWIPs and seven XWIPs) were measured within 3 to 5 h, resulting in one measurement every 12 to 20 min. The raw aggregated measurements and the correction procedure are described in Appendices  and . Some short-term fluctuations in the high-frequency data caused by diel air temperature fluctuations could be observed that could not completely be removed by the postprocessing procedures. Due to the large number of data points in the full data set and our interest in the overall temporal dynamics, we limited our further analysis to daily median values of the full data set, setting aside the development of a more robust diel calibration procedure for future studies.

Three of the xylem probes (T1B, T2B and T3B) exhibited a negative δ18O bias, which was corrected as described in Appendix . A comparison of the probe heads right after removal from the stem (12 weeks after installation) revealed that the membrane heads of two δ18O-biased probes were covered by biofilms while an unbiased probe did not show such a biofilm (see Fig. ).

Focusing on the first period, between 21 May (date of the irrigation) and 10 June, the soil δD signature was rather stable, while δxyl increased for 6 to 14 d to reach a plateau. The δD signatures at the stem base at 10 cm height (green triangles in Fig. c and d) showed the steepest rise and reached their plateaus after approximately 6 d while the probes installed at 8 m height (pink triangles in Fig. ) showed a delay of around 14 d. The δD signatures at 1.5 m tree height (yellow symbols) responded in between the former two groups.

The immediate post-irrigation δ18O signatures of the soil profile showed no considerable depth differentiation and little dynamics (see Fig. c). Following some smaller precipitation events with elevated δ18O signatures (-7.2 ‰ in rain compared to -9 ‰ in the soil), the soil signatures slightly shifted upwards. A similar development can be observed for the xylem δ18O signatures following the soil signatures. The larger rainfall event in the night between 10 and 11 June, followed by another 13 mm event on 15 June, influenced the soil isotopic signatures in two ways: the upper 20 cm of the soil was enriched in δ18O (2 ‰ to 3 ‰ more enriched than the lower soil depths), and the δD-enriched label water introduced with the irrigation was percolated further downwards. Following those changes in the soil isotopic signatures, we see the xylem δ18O signatures increasing by about 1.5 ‰ within 5 to 10 d. Simultaneously the xylem δD signatures decrease to levels close to the topsoil δD signatures.

We observed two periods 23 June to 11 July and 16 to 26 July that are characterized by declining soil moisture and rather constant δsoil. Both of these periods show the same pattern of δxyl further deviating from the isotopic composition of the topsoil and converging towards the values of the deeper soil layers. On the other hand, we also observed two rainfall events (12 and 27 July) that lead to a replenishment of soil moisture without considerable changes in δsoil. In both cases, we could see an opposite response to the dry period. δxyl was more similar to the isotopic composition of the upper soil layers and diverged from that of the deeper soil layers. The 18 mm of rainfall on 12 July was exhausted within the following days, and soil moisture (and δ18O signatures) quickly returned to the low levels before the event. The rainfall event on 27 July raised the soil moisture levels to such an extent that the low pre-event soil moisture did not recur within the observed time period.

The temporally and spatially continuous soil moisture and soil water isotope data needed for the optimization of the RWU model were obtained by interpolation of soil sensor data, soil core measurements and SWIP measurements (see Fig. ).

Subsequently, the optimization was carried out as described in Sect. . Figure  shows the results for the combined parameter optimization of the RWU model and the transfer function hR, which is used to convolve the modeled δxyl.RWU in order to obtain values for validation of δxyl.R. Each row in Fig.  belongs to one model output variable (δ18O, δD and the RWU depth distribution index rU) and was evaluated individually. The best 10 model simulations are depicted in blue, and 20 random samples drawn from the worst 50 %–90 % of all simulations are depicted in red/orange. The evaluation was done for the starting phase (dark blue and red) and for the full observation period (light blue and orange).

When only the first half of the observational record is considered (darker blue squares and lines), both isotopes show a parameter optimum for zr (rooting depth parameter) between 0.75 and 1 m (see Fig. d and h). For that period, it was not possible to identify the optimal parameter value for the other two (water-stress-related) RWU parameters θw and θ‾c1, which seemed to be rather insensitive to both isotopes (see dark blue squares in Fig. e, f, i and j).

The maximum lateral root extent rmax was critical to reproduce the rise of the deuterium signal after the irrigation and showed a clear optimum around 3 m (Fig. k). The lateral root density decay parameter λ (not depicted in Fig. ) proved to be far less sensitive than rmax, but there was a clear tendency towards values of λ below 1, implying a faster-than-linear decrease in horizontal root densities. When the full time period was considered (light blue diamonds and lines), the optimal values for zr were found at deeper depths between 0.9 and 1.5 m (see Fig. d and h). The optimal wilting point soil moisture θw ranges between 6 %–8 % and 7 %–9 % (for δ18O and δD, respectively; see Fig. e and i).

Unlike the two water isotopes, the water uptake ratio rRWU relies on soil moisture data alone and is not involved in the convolution step. Consequently, rmax was completely insensitive to rRWU. With respect to rRWU, optimal zr values were found between 80 and 100 cm, which is in good agreement with the isotope-based zr values in the start phase of the observational record. Based on rRWU, the optimal θw values are between 7 % and 9 % (see Fig. m), and the optimal θ‾c1 values are between 30 % and 100 % (see Fig. n).

Based on the optimized RWU model, we could compare modeled δRWU to measured δxyl values. Except for the deuterium signatures towards the end of the experiment, there was a good agreement for both isotopes (see Fig. ). However, in cases of abrupt δRWU changes, the observed δxyl values did respond with a delay which increased with stem height. This was most obvious after the deuterium labeling (box A in Fig. b). In order to account for the expectable delay that occurs during the transport of water from the roots along the xylem, we optimized FPLDs to transform our modeled δRWU values into δxyl values.

Figure  shows observed (squares) and modeled (lines) δRWU (grey) and δxyl (green and pink) values. The original time series was transformed into the sap distance domain (see Sect. ) in order to eliminate the influence of time-variable vsap, which was lower at the start of the depicted period and higher towards its end. Figure b depicts the same data as Fig. a but plots their rate of change instead of their absolute values. The colored lines in Fig. a and b are the results of convolutions of the modeled δRWU signature with different FPLDs (depicted in Fig. c).

In order to transform δRWU into δxyl.R, we convolved it with two different transfer functions: (1) the conceptually grounded hR (thin green line, defined in Sect. ), whose parameters were optimized together with the RWU model parameters, and (2) the empirically, more flexible hF1 (thick green line, defined in Eq. ), whose parameters were optimized subsequently to reach the best possible fit to observed δxyl.R values. The overall shapes of hR and hF1 turned out to be similar, but the latter achieved a much better fit to the available δxyl.R observations, while the former failed to adequately reproduce the right-skewed, tailed shape required to fit the observational data (see Fig. b).

Following this, we simulated the signal transformation of δxyl.R (at the stem base, thick green line) into δxyl.H (at 8 m stem height, thick pink line) by convolving δxyl.R with another transfer function, hF2 (dashed pink line in Fig. c), whose parameters were optimized to reach the best possible fit to observed δxyl.H values. In contrast to hF1, hF2 features a notable time lag around 1.4 m at the beginning and has a strong peak. Its tailing is similar to that of hF1.

To directly transform δRWU into δxyl.H, it can be convolved with hF1F2, which is the convolution of the two FPLDs hF1 (root tips to stem base) and hF2 (stem base to 8 m stem height).

According to the shape of hF2, the largest fraction of a signal between the stem base and a stem height of 8 m arrives after 1.4–2 m of cumulative sap flow distance. This may seem like a paradox, but it is not. The sap flow distance s is derived from heat-probe-based vsap, which other studies have reported to be considerably lower than vδ (transport velocity inferred from isotopic tracer observations). Based on our observations, we can infer vδ between the stem base and 8 m stem height to be about 5.5 times faster than vsap.

In order to compute temporally variable distributions of xylem water ages at a certain stem height, two things were required: (1) a transfer function representing the FPLD between root tips and the stem height of interest, i.e., hF1 and hF1F2 as determined within the previous section and (2) a sap flow time series.

We extended our measured sap flow time series beyond its original range over a full year as described in Sect.  (see Fig. b for the complete extended vsap time series). Subsequently, we duplicated this extended vsap time series in order to obtain enough data for an appropriate warm-up period for the following computations.

By combining sap flow velocities, FPLDs, and virtual tracers for each day (as described at the end of Sect. ), we obtained xylem water age distributions at 0.1 and 8 m stem height. In Fig.  the time variable age distributions are represented through specific quantiles between 0 % and 99 % for 8 m stem height. For clarity's sake, only the median water age is depicted for 0.1 m stem height.

Figure a shows the xylem water ages over the course of a year between the ends of two vegetation periods. During the dormant season (November–May) xylem water is immobile, and consequently its age increases by one day per day, eventually exceeding ages of 200 d and more. At the start of the growing season, xylem water ages drop sharply, as soon as fresh uptake water has replaced the previous season's water, which happens earlier at the base of the tree stem.

Figure b focuses on the growing season of our field experiment. At the start and towards the end of the growing season, xylem water ages are considerably larger than during the main growing season. From the beginning of June to the middle of September the median xylem water age at 8 m stem height varies between 2.3 and 8 d with a mean value of 4.7 d. Median xylem water ages at 0.1 m stem height in the same period are lower and range between 0.4 and 3.8 d with a mean value of 1.6 d.

By complementing the measurement system of with a sophisticated hard- and software framework to control the required gas flow controllers and solenoid valves, we developed a system capable of largely unattended long-term operation. As all of the additional components were built from readily available parts, our extension of the original setup did not notably increase the overall cost, which is mainly set by the CRDS itself and to a smaller degree by the required probes and valves.

Up to this date, our setup is the most complete field-tested in situ stable water isotope measurement system for continuous ecohydrological investigations. It contains many of the elements of the “ideal system” sketched by . To summarize, we list the main advantages of the use of WIPs compared to other in situ measurement techniques.

To install WIPs into the soil, it suffices to dig or drill a hole with a diameter of around 30 cm. Multiple WIPs (in different depths, at different sectors of the hole) can then be pushed into practically undisturbed soil. The installation of loops of gas-permeable tubing into the soil, as used by , , and , is much more invasive and will inevitably disturb the observed soil to a higher degree.

We encountered some issues with partially biased δ18O XWIP measurements, similar to what have reported. Since not all XWIPs exposed such a δ18O bias, we hypothesize that the occurrence of the encountered bias is related to the observed formation of biofilms on the XWIP probe heads (see Fig. ). Those biofilms might have promoted the emission of volatile organic compounds which have been reported to interfere with CRDS stable water isotope measurements . However, even when the δ18O measurements seemed biased, they exposed similar temporal dynamics as unbiased measurements, and all of those dynamics agreed with what our proposed modeling framework predicted. So even though we may not be completely sure how to reliably rule out the formation of δ18O-bias-inducing biofilms, which are potentially favored by the design of our probes compared to the more aerated approach of , we are confident that the observed temporal dynamics will still contain valuable information. If unbiased xylem measurements or observations of soil isotopic data are available, a bias correction should always be possible.

Considering the expected spatial heterogeneity of a skeleton-rich, clayey soil – on top of the spatial heterogeneity of infiltration patterns within forest stands – and the relatively slow temporal dynamics of the observed soil isotopic signatures, future investigations might benefit from an increased number of WIP soil profiles at the cost of a lower temporal resolution of soil isotope measurements.

Our standard probes were sampling the vapor from the headspace of sealed containers filled with waters of known isotopic composition. This contrasts to other practices of using soil standards , prepared from dried soil material that was rewetted with standard water. The main reason of using headspace standards was the situation that the maximum number of WIPs in our setup was limited and that such soil standards may not be representative for xylem isotope measurements. Furthermore, the sampling of field soil for a “representative” soil standard is problematic when soil properties vary with depth – a standard suited for one horizon may lead to biased results for another horizon. Furthermore, have shown that clay minerals may lead to isotopic fractionation when labeled water is applied to oven-dried clay-rich soils. This might lead to biases that are difficult to attribute to the different samples, and hence liquid water standards may be the better choice.

For a WIP with fixed dilution rate placed in the headspace of a liquid water standard with variable temperatures, we found a close relationship between the sample gas' vapor concentration and isotopic composition (see Fig. ). As long as the air entering our probes is vapor saturated (which has been shown to be the case for soils by , while have computed very fast saturation within the tree xylem), the sample gas vapor content is directly related to the temperature of the sampling location. Therefore, we ended up with a calibration procedure that uses the sample gas vapor concentration, which is automatically measured by the CRDS, instead of measured temperatures at the sampling locations. When all measurements of one probe per day were averaged, the resulting time series were reasonably consistent on a day-to-day scale. On a shorter timescale we observed fluctuations (for xylem and soil probes, but with clearly more pronounced fluctuations for soil probes closer to the surface), which were likely artifacts of insufficiently compensated temperature effects. A calibration procedure that explicitly considers observed temperatures at each WIP might help to dissolve these sub-daily fluctuations and therefore improve the measurement accuracy and enable the exploitation of the full temporal potential of these high-frequency in situ measurements. But the proper consideration of temperature effects is difficult under field conditions, especially when considering tree stems, where strong temperature gradients can occur at small spatial extents (see ). Even for laboratory conditions, reported a mismatch between their measurements and the equation to compute the isotopic fractionation between the liquid and the vapor phase under equilibrium conditions as a function of temperature.

We were able to identify meaningful parameters (zr, θw and rmax) for our process-based RWU model. This model in turn was suited to predict δRWU. Our approach of driving the RWU model directly with (interpolated) measured data avoided the difficulties that are likely to occur during the simulation of water transport within highly structured, skeleton-rich soil. Yet, our data-driven approach prevented problematic parametrizations of the RWU model from accumulating errors over consecutive time steps as would happen when the model itself had to keep track of soil moisture and soil water isotopic composition. Consequently, the critical model parameters θw (wilting point) and θ‾c1 (onset of uptake reduction) were not identifiable (θw was insensitive when optimized against isotope data but was identifiable when optimized against soil moisture).

Regarding the RWU δD signatures, there is a notable mismatch for the second half of our observation period: the model systematically predicts more enriched δRWU values than we could measure at δxyl. Since all of the measured soil δD values during that period were more enriched than the observed δxyl, this is not a failure of the model itself, but rather a consequence of insufficient model input data. This could hint at deeper uptake depths which were not covered by the SWIP depth profile, the general lack of representativeness of one single SWIP profile due to soil heterogeneity or in the worst case a systematic bias in XWIP δD measurements as an aftereffect of the 10 d measurement interruption in July.

Unlike most hydrological catchments, where FPLDs change with the length of the flowing stream network , the tree xylem may be considered to feature a static FPLD which is constant irrespective of the occurring transport velocities. Consequently, xylem water ages are determined by a static FPLD and time variable tracer transport velocities (vδ). While it is nearly impossible to monitor vδ with a high temporal resolution, vsap can be used as a proxy for vδ.

Previous experiments have shown that vδ may exceed vsap by several hundred percent. reported vδ to be 5 times higher than vsap, and even reported it to be about 16 times higher than vsap. In controlled laboratory experiments, observed gravimetrically determined flux rates to be 3.7 times higher than heat-pulse-derived vsap without wounding correction (which we also did not apply). In order to derive vsap from heat pulse probe measurements, a value for the thermal conductivity of sapwood (see Eq. ) is needed. We took this value from another publication , but we cannot be sure whether the used value is actually appropriate as the authors of the cited study did not specify how they came to this value. Additional assumptions would be necessary for the wounding correction, but as reported, the heat pulse method can be expected to underestimate actual flux rates even after the wounding correction.

Regarding all these complications to relate heat pulse base estimates of vsap to actual flux velocities, we can say that it is no surprise that we observed a mismatch between vsap and vδ. On top of that, heat-pulse-based estimates of vsap are based on point observations from a limited number of depths (in our case 5, 17.5 and 30 mm), whereas the actual sap flux has a continuous depth profile of varying velocities . Our WIPs sample the xylem from 0 to 50 mm depth, which in case of a distinct velocity gradient within that range might lead to a disproportional weighting of the actual sap flux passing the probe.

Nevertheless, the studies of and indicate that vsap measurements should be a good proxy for fluctuations of vδ, even though the actual values can be expected to be scaled differently. The discrepancy between the fitted γ value of 1.43 m of hF2 in the sap flow domain (see Fig. c) and the corresponding real-world distance of 7.9 m between stem base and 8 m stem height is a consequence of the systematic underestimation of vsap due to the discussed issues with heat pulse probe methodology. Consequently, all of the fitted FPLDs should be rescaled by a factor of 5.5. However, as long as the only goal is to account for relative differences of flow velocities (opposed to the attribution of certain physically observable properties to the shape of the fitted FPLDs), the scaling factor between actual and apparent vsap is irrelevant.

Our conceptually derived hR, which was based on assumed vertical and lateral root distributions, proved suited to act as FPLD between δRWU and δxyl.R Yet, due to a lack of observations of lateral root distributions, we had to estimate an appropriate value for the maximum lateral root extent rmax via model parameter optimization, where rmax was identifiable when the model was evaluated with respect to δxyl.R. Given the uncertainties arising from measurement precision and accuracy, as well as spatial heterogeneity of the soil, it turned out that the robustness of an rmax estimate greatly improves with a distinct artificial isotopic labeling pulse.

However, the overall shape of the conceptually derived hR was unable to fully reproduce the skewness and tailing of the fitted parametric distribution hF1 (from Eq. ), which produced an even better fit to the observed data. The observed tailing might be a consequence of an unexpected lateral root distribution, but it is more likely to be caused by dispersion during the root xylem passage, which is not directly accounted for within the applied convolution modeling approach. Other than the conceptually based hR, the distributions that can be achieved with different parametrizations of Eq. () (i.e., hF1 and hF2) seem to be able to implicitly account for the supposedly observed dispersive component of the tracer transport – at the cost of the interpretability of the optimized parameters. More elaborate modeling approaches that explicitly account for the effects of dispersion and diffusion should be able to yield both: physically meaningful model parameters and a good fit between simulated and observed tracer time series. Yet, such explicit modeling approaches would quite likely have a much higher computational cost than our simplified convolution approach and might require more extensive input data.

Future labeling experiments with sequentially applied tracer pulses limited to certain radial distances from the stems of trees with different characteristics, combined with more process-based modeling approaches, could help to study macroscopic and microscopic factors that shape the FPLD of a tree's root xylem.

During the main growing season 50 % of all xylem water passing the stem base of our studied beech trees was older than 1.6 d. When looking at the 8 m stem height, the mean median xylem water age was 4.7 d. Assuming the xylem water transport velocities are not changing fundamentally above that point, we can estimate that the mean median water age of the xylem water within the tree crowns of our studied trees was close to 10 d. Towards the fringes of the growing season, we can expect considerably higher water ages. This has to be kept in mind for any type of xylem water sampling in order to investigate RWU, specifically after rainfall events or artificial isotopic labeling, but also during periods where water stress may lead to changes in δRWU.

Previous studies have typically investigated aboveground xylem water transport via injection of isotopic tracers into the stem, and they gathered valuable data regarding the transport processes between the stem base and crown branches or leaves. However, by injecting their tracers above the ground, they did not capture the below-ground component of xylem water transport, between all individual root tips and the stem base.

, citing the study of , claimed they had “estimated time lags between RWU and transpiration”, while they had actually estimated time lags between tracer injection to the stem base and transpiration. Similarly, propose a modeling framework that erroneously equates δRWU to δxyl at the stem base, leading them to the prediction of unlikely clear δxyl signals further up the stem. The FPLD between root tips and stem base (hF1 in Fig. c) contributes considerably to the smoothing of δRWU, much more than the FPLD along the first 8 m of stem height (hF2 in Fig. c). Consequently, we strongly suggest including the below-ground fraction of the tree in any endeavor that aims to simulate the propagation of δRWU along the stem.

At that point, it is important to note that most of the root system FPLD's distribution form results from its spatial configuration, featuring not only a depth density distribution, but also a lateral abundance (lateral density combined with projected area) distribution. Nevertheless, the often used simplified vertical 1-D representation of the soil–plant system for RWU investigation purposes does not necessarily have to be expanded by a second dimension: a computationally efficient way to account for vertical and lateral root distributions can be achieved by convolution of δRWU with an appropriately shaped FPLD.