Temporal dynamics of tree xylem water isotopes: In-situ monitoring and modelling

We developed a setup for a fully automated, high frequency in-situ monitoring system of the stable water isotopes Deuterium and O in soil water and tree xylem. The setup was tested for 12 weeks within an isotopic labelling experiment during a large artificial sprinkling experiment including three mature European beech (Fagus sylvatica) trees. Our setup allowed for one measurement every 12–20 minutes, enabling us to obtain about seven measurements per day for each of our 15 in-situ probes in the soil and tree xylem. While the labelling induced an abrupt step pulse in the soil water isotopic signature, it 5 took seven to ten days until the isotopic signatures at the trees’ stem bases reached their peak label concentrations and it took about 14 days until the isotopic signatures at 8 m stem height levelled off around the same values. During the experiment, we observed the effects of several rain events and dry periods on the xylem water isotopic signatures, which fluctuated between the measured isotopic signatures observed in the upper and lower soil horizons. In order to explain our observations, we combined an already existing root water uptake (RWU) model with a newly developed approach to simulate the propagation of isotopic 10 signatures from the root tips to the stem base and further up along the stem. The key to a proper simulation of the observed short term dynamics of xylem water isotopes, was accounting for sap flow velocities and the flow path length distribution within the root and stem xylem. Our modelling framework allowed us to identify parameter values that relate to root depth, horizontal root distribution and wilting point. The insights gained from this study can help to improve the representation of stable water isotopes in trees within ecohydrological models and the prediction of transit time distribution and water age of transpiration 15 fluxes.


Introduction
Transpiration from terrestrial plants is a key component of the global hydrological cycle and its fraction of the total water balance might even increase under projected future climatic conditions (Bernacchi and VanLoocke, 2015). Process based ecohydrological models can be an important tool to gain realistic estimates of the vegetation's response to climatic changes. 20 Such process based models need detailed data on plant water uptake and transpiration. These processes can and have been studied intensively with the help of stable water isotopes (White et al., 1985;Calder, 1991;Dawson and Ehleringer, 1991;Busch et al., 1992;Ehleringer and Dawson, 1992;Zhang et al., 1999;Dawson et al., 2002).

Isotope tracer enhanced observations of tree water dynamics
To observe the temporal dynamics of water within the soil-plant-atmosphere continuum (SPAC), isotopic labelling experiments 25 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 (δ T ) following isotopically labelled irrigation pulses (e.g. Yepez et al. (2005); Volkmann et al. (2016a)). 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 30 (Evaristo et al., 2019) and in a Central European forest with grown, 25 m high, specimen of Fagus sylvatica and Abies alba . Instead of chamber measurements of δ T , they extracted water from tree crown branches to monitor the isotopic composition of xylem water (δ xyl ). For seven months, Evaristo et al. (2019) had a weekly δ xyl sampling scheme, while Magh et al. (2020) started with a sub-daily δ xyl sampling scheme for five days and continued the following two month with a sampling frequency of four to six days. Both experiments observed notable delays (days to weeks) between tracer application 35 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 D 2 O into the stem base (James et al., 2003;Meinzer et al., 2006;Schwendenmann et al., 2010;Gaines et al., 2016). Due to the high Deuterium concentrations of the injected label, tracer breakthrough curves within the tree crown could be acquired by analysing condensate from branch or foilar samples placed into zipper bags. Time delays between tracer 40 application and maximum tracer concentrations within the tree crowns mostly have been reported to amount to a few days, but for a 50 m high specimen of Tsuga heterophylla Meinzer et al. (2006) also reported a delay of about 30 days. 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 (Meinzer et al., 2006;Gaines et al., 2016).
1.2 Water uptake and tree isotope modelling and treatment. The required effort per sample and the disturbance caused by each sampling limits 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 not any longer require the extraction of 80 liquid water samples. Instead, the isotopic composition of the vapour contained in a gaseous sample can directly be analysed 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 (Wassenaar et al., 2008;Garvelmann et al., 2012). 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 85 Beyer et al. (2020).
Different approaches for in-situ measurements of δ soil have been proposed and tested by Soderberg et al. (2012), Rothfuss et al. (2013), Volkmann and Weiler (2014) and Gaj et al. (2016). So far the method of Rothfuss et al. (2013) has seen the most subsequent applications ranging from long term, continuous lab-experiments (Rothfuss et al., 2015) to campaign based field studies (Oerter and Bowen, 2017;Kübert et al., 2020). For in-situ sampling of δ xyl , Marshall et al. (2020) developed the bore hole 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 tree logs and in a greenhouse experiment with small trees placed in pots filled with water instead of soil.
The in-situ probes developed by Volkmann and Weiler (2014) are the only approach that has been proven to work in soil (in six two-day sampling periods, Volkmann et al. (2016a)) as well as within tree xylem (in two young Maple trees over 11 days, 95 Volkmann et al. (2016b)). 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.
This study's primary motivation was to test out the automated measurement setup in a prolonged field experiment. Never-100 theless, the results of our WIP measurements and the subsequent analyses could also be used to scrutinize the following two hypotheses regarding tree water isotope dynamics and transit times: 1. Xylem water isotopic signatures are equivalent to the isotopic signature of root water uptake.
2. The spatial distribution of a tree's root system has an effect on the shape of the xylem water age (i.e. time elapsed since uptake) distribution, which in turn can be used to infer information on that spatial distribution of the root system. The isotopic concentration of root water uptake (δ RWU ) for either 18 O or Deuterium can be computed with the following equation: where i is the index of a specific soil layer, N is the total number of all soil layers, δ i is the soil water isotope signature and ∆z i the thickness of soil layer i. According to Jarvis (1989), S i is the relative sink strength of the soil layer i which is defined by: where R i is the proportion of total fine root length within layer i and α i is a stress index. Following a root distribution model introduced by Gerwitz and Page (1974), Jarvis (1989) defined R i as: where θ i is a soil layers volumetric water content, that lies between wilting point θ w and saturation θ s .

Flow path length distribution
Root water uptake (RWU) happens at different depths and different radial distances from the stem base. An isotopic signature measured at the stem base will consequently represent a mixture of waters transported over various distances (or flow path 130 lengths) from the root tips to the stem. The flow path length distribution (FPLD) of a tree root system is determined by (1) a vertical component f (z), depending on the soil depth z and (2) a radial component g(r), depending on the radial distance from the stem center r.
The depth dependent RWU probability function f (z) can be defined by a mathematical function (like in Eq. 3) or by empirical data of vertical fine root density distributions. The radial RWU density function g(r) is, however, much less reported 135 and studied. In most cases, RWU is considered from a one dimensional perspective with regard to depth alone. For our purposes we are also interested in the distribution of fine roots regarding the radial distance from the stem. Due to a lack of reported observational data, we propose the following equation to describe the relative root density (integrated over all depths) along a radial transect between the centre of the stem (r = 0) and the maximum radial extent of the rooting system (r = r max ): where the radial density of roots decreases linearly towards the outer extent of the rooting system when distance decay parameter λ = 1 and slower for λ < 1. In order to account for the effect of the projected area of a certain distance class, g(r) is computed according to: where the denominator term normalizes the integral of g(r) within 0 ≤ r ≤ r max to unity. With the vertical component f (z) and the radial component g(r) defined, both can be combined into a probability density function of RWU h R (z, r) in the following way: where z 1 , z 2 , . . . z i−1 , z i and r 1 , r 2 , . . . r j−1 , r j denote sufficiently fine spaced values of z and r within the respective domains of f (z) and g(r). Now we can use the Pythagorean theorem to compute the total distance to the stem base and aggregate h R (z, r) to the flow path length distribution h R (s): , for all z and r that fulfill z 2 + r 2 = s (9)

Signal transformation and convolution
Inspired by a long line of tracer hydrological research (e.g.: Małoszewski and Zuber (1982); Kirchner et al. (2000); Weiler et al. (2003); McGuire and McDonnell (2006)) that uses convolution integrals to transfer precipitation tracer time series to stream 155 tracer time series via a transfer function, we adapt this approach to model the tracer dynamics within the tree xylem.  In order to neutralize the effects of sap flow velocity variations we transform our observed tracer time series δ(t) to "sap distance series" δ(s). This transformation is depicted in Fig. 1 and it requires to obtain a cumulative sap flow distance s for each time step p t with the following equation: where ∆s i is the distance travelled by the sap during t i , and ∆v i is the mean sap flow velocity of t i , which has a duration of ∆t i . With an established transformation between time t and sap flow distance s, we can transform observed tracer time series δ(t) to tracer "sap flow distance" series δ(s).
After the transformation of δ(t) to δ(s), we can predict the isotopic signature at the stem base, δ xyl.R , by convolving δ RWU with the FPLD between the stem base and all root tips (e.g. h R from Sec. 2.1.2): Similarly, we can relate δ xyl.R to δ xyl.H (an isotopic stem xylem signature at a certain height above the stem base) by convolution with an appropriate transfer function that manages to represent the respective FPLD.
Eventually the methodology described in the previous sections can be combined as follows: A sketch of the experimental setup is shown in Fig. 2, which omits the repeated instances of the principal components and sensors. Precipitation (throughfall) samples were taken as often as possible from four rain gauges (  T1H), where R stands for "root" (10 cm), B for "breast height" (150 cm) and H for "high" (800 cm). Depending on the locations of the probes and the trees, the tubing lengths between the probes and the CRDS varied between 5 m (T2R and T2B) and 20 m (T1H). Additionally, we put two probes into the head space of two sealed 1-Liter containers made of high-density polyethylene (HDPE), filled with 250 mL of water with known isotopic composition ( Fig. 2.E). These two probes acted as our light (δ18O = -11.61‰, δD = -82.4 ‰) and heavy (δ18O = -0.93 ‰, δD = 6.63‰) reference standards and were placed directly next to the 195 CRDS in our field lab.
In order to install the WIPs with a diameter of 10 mm into the tree xylem, we drilled a hole with a 10 mm wood drill, a strip of tape marking a hole depth of slightly more than the length of the 5 cm porous head. Care was taken, not to overheat the drill in order to avoid singed xylem wood in the hole. Afterwards, a 10.2 mm metal drill was used to slightly widen the hole and clear out wood chip residue. Then the probe was firmly pushed into the hole just deep enough to place the porous head behind the the phloem. In a final step, silicone was applied around the probe to seal the hole. While the silicone is curing, organic fumes may interfere with the measurements of the CRDS. Therefore it is advisable, to install the probes several days before the scheduled start of the measurements. In addition, we placed heat pulse based sap flow sensors (East 30 Sensors, Pullman USA) in the vicinity of each WIP. Measurements of the tipping bucket, soil moisture sensors and sap flow sensors where logged in 10 minute intervals with a CR1000 data logger (Campbell Scientific, USA).

Tracer Experiment
The stable water isotope concentrations for 18 O and Deuterium in this paper are noted in the δ-notation relative to Vienna standard mean ocean water (VSMOW): where R sample and R VSMOW are the D/H or 18 O/ 16 O ratios of the sample and VSMOW, respectively.

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Since not direct water source was available to irrigate the plot with a defined amount of 150 mm, 60 m 3 groundwater were trucked to the site, run through an industrial deionizer (VE-300 (6x50 Liter), AFT GmbH & Co.KG) to reduce the mineral content to low levels typically found in natural rainfall. In our case the sprinkling water had an electrical conductivity of around 20 µS/cm and a isotopic composition of (δ 18 O = -9 , δD = -63 ). By mixing 1 kg of D 2 O with the 60,000 Liters of water within a collapsible pillow tank (custom made by Faltsilo GmbH, Bad Bramstedt, Germany), which was placed 100 215 m upslope of the experimental plot, we obtained Deuterium enriched irrigation water (δ 18 O = -9 , δD = 40 ). On 21 May 2019, we used an array of 6 sprinklers (XCEL-Wobbler by Senninger, Clermont, USA) driven by the height difference between pillow tank and irrigation site, to distribute our prepared D 2 O-groundwater-mixture onto the experimental plot. The amount of irrigation water actually reaching the core plot area of 10 by 20 m was equivalent to 150 mm rainfall within 8 hours. After this artificial event, we continued to monitor the plot under natural conditions for another 12 weeks.

Stable water isotope measurement system
On two days prior to the irrigation, as well as one day after the irrigation, we took a total of five destructive soil core samples.
We used an electric breaker (HM1812, Makita Werkzeug GmbH, Germany) to drive a core probe (60 x 1000 mm, Geotechnik Dunkel GmbH & Co. KG, Hergolding, Germany) into the soil until we hit larger rocks. The soil cores were extracted and split into 10 cm segments, yielding 120 to 300 g of fine soil and skeleton material per depth increment, that were filled into 225 aluminum coated coffee bags (WEBAbag CB400-420siZ, Weber Packaging GmbH, Güglingen, Germany).
Following the equilibration bag method after Wassenaar et al. (2008) and Garvelmann et al. (2012), the sample bags were filled with dehumidified air in the lab and permanently sealed with sealing tongs (Weber Packaging GmbH). After 24 hours of equilibrium at constant temperature, the sample bags were punctured by a hollow needle connected to the inlet port of a Cavity Ring Down Spectrometer (CRDS) stable water isotope analyser (L2120-I, Picarro, Santa Clara, USA). After five to ten soil bags, we also measured three standard bags filled with liquid water of known isotopic composition, which were treated identical to the bags containing soil samples.
The WIPs used in this study were build at the Chair of Hydrology of the University of Freiburg, Germany, following the "diffusion-dilution sampling" (DDS) design described by Volkmann and Weiler (2014). Figure 3 shows a sketch of a WIP in-235 stalled into the soil. Key element of a WIP is the mixing chamber (custom product manufactured by Horst Fischer GmbH, Gundelfingen, Germany) right behind the porous membrane head (custom product manufactured by Porex Technologies, Aachen, Germany), where a dilution line dilutes the sample gas in order to prevent condensation within the sampling line on its way to the isotope analyser. The additional through flow line compensates for any pressure differences arising from dilution rates that are smaller than the isotope analyser's sample rate and to allow for flushing the system with dried air.  Over custom manufactured valve manifolds (Horst Fischer GmbH, Gundelfingen, Germany), equipped with 2-way electric valves (EC-2M-12, Clippard, Cinncinati, USA), each of the probes was connected to the two mass flow controllers and the sample inlet of the field deployed CRDS stable water isotope analyser (L1102-i, Picarro, Santa Clara, USA). Connections 250 between the probes, valve manifolds, mass flow controllers and isotope analyser were made with 1/16" FEP (inner diameter = 0.75 mm) tubing (Techlab GmbH, Braunschweig, Germany) and Flangeless Fittings (XP-220, IDEX, Lake Forest, USA).
Connections between the dry air supply and the mass flow controllers were made with stainless steel fittings (Swagelok, Solon, USA). We set up our field deployed CRDS and its peripherals within a watertight container and supplied it with electricity from a nearby power line.

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Based on the Arduino microcontroller platform, we designed and built a custom circuit board that is able to switch electromagnetic valves and to provide two independent analogue voltages. Those voltage signals were used to control the throughflow of two mass flow controllers. A custom made Python based software GUI that is able to interface the Arduino based circuit board and interpret the CRDS' log files near real time enabled us to automate the measurement process to a large extent and to quickly adapt flow rates and times for flushing and measuring as well as the order of the probe sequence. We attached a USB-260 modem (E531, Huawei Technologies, Shenzen, China) to the isotope analyser to regularly transmit summarized measurement results (less than 20 kB/h) to an ftp-server. With this setup, we could remotely monitor, but not interfere with the ongoing measurements. Further details on this automation system (circuit board designs, assembly instructions and source codes of the control software) can be found in in the following online repository: https://github.com/stseeger/IsWISaS.
In order to obtain a measurement value for a certain probe, we activated the three respective valves of that probe (sample, 265 dilution and through-flow line). The time of activation was saved to an automatically generated log file. At the same time, we initiated a flush phase by setting the dilution rate to the same as the CRDS' sample intake rate (in our case 35 mL/min) and setting the flow rate in the through-flow line to zero. The duration of the flush phase was chosen depending on the overall tubing length of the probe -from three minutes for probes with short tubing, up to ten minutes for probes with 20 m long tubing.
After the flush phase, we started the measurement phase by reducing the dilution flow rate to 10 mL/min and increasing the  Table 1. The standard deviation s was computed as: where N is the number of raw instrument readings within th last two minutes, x 1 , x 2 , ..., x N are all of the respective values and x the mean of all these values. With the value of N/2 rounded to a whole number, the trend index I T was computed as: probe sequence, which was automatically restarted upon its completion.

Data processing
From the raw sensor data, we computed the sap flow velocity v sap in m/s according to Campbell et al. (1991): where k is the thermal conductivity of sapwood set to 0.5 W m -1 K -1 (Hassler et al., 2018), C w is the specific heat capacity of 285 water at 4.184 × 10 6 m 3 K -1 , r u and r d (both = 6mm) are the distances of the central heater needle to the up-and downstream thermistor needles and ∆ T u and ∆ T d 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).

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During those periods, we set v sap to 0 m/s. For the remaining period between 8 August and 31 October, we fitted the two parameters a and b of the following equation: 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 v sap due to leaf senescence, we multiplied the estimates 295 obtained by Eq. 2.3 with a linearly decreasing reduction factor between mid of September and end of October. Urban et al.
(2015) reported a comparable autumnal reduction of sap flow in relation to potential evaporation for Central European beech trees.
As an additional mean to investigate RWU independently of isotope measurements, we followed Guderle and Hildebrandt (2015) and used measurements of volumetric soil moisture -more specifically the daily decline of soil moisture during dry 300 days -as an indicator of RWU. To compare the soil moisture measurements with the RWU model, we derived a water uptake ratio r RWU in two ways: where the first ratio defines the measured daily decline of soil moisture at the upper soil layer ∆ θu (average of 10 and 20 cm depth) and ∆ θl the equivalent for the lower soil layer (average 40 and 60 cm depth). The second ratio defines the relative 305 modelled uptake strengths of Eq.2 (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 r RWU is limited to days where the soil water content throughout the depth profile is below field capacity.
In order to analyse 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 two minutes of each period. The parameters of interest were sample water vapour content, δ 18 O and δD. In the next step we corrected for the influence of temperature on the fractionation factors during vapour 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 vapour content of the obtained sample gasgiven that the sample rate and the dilution rate are held constant. By computing linear regressions between measured vapour isotope values (δ m ) for our two standards and the sample gas moisture contents (C m ), we derived the slopes needed to correct 315 all vapour isotope measurements to one reference moisture content value (C r = 18000 ppmV) according to the following equation: where δ v is the corrected isotope value and ∆ Cδ is the slope obtained by the linear regression between C m and δ m values of the standards.

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To infer the isotopic signature of the liquid water that equilibriated with the sampled vapour, we used the relationship between the known liquid phase values of our two standards and the respective observed vapor values: where δ l.x is the normalized liquid phase isotopic value of measurement x, δ v.x is the moisture corrected vapour value of measurement x, δ v.L is the moisture corrected vapour value of the light standard, δ l.L , is the liquid phase isotopic value of the 325 light standard and ∆ LH is the slope obtained by: with δ v.H as the moisture corrected vapour value of the heavy standard and finally δ l.L and δ l.H as the known liquid water isotope values of the light and heavy standards, respectively.
Under stable environmental conditions, δ v.L and δ v.H should not change at all, but in a field experiment more frequent 330 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 three to four hours. For the normalization procedure we interpolated between those actually measured standard values in order to estimate the standard values for each measurement.

Modelling RWU, FPLDs and xylem water age
To obtain the necessary input data for RWU modelling, we interpolated our observations of volumetric soil moisture and soil was evaluated by computing the the root mean square error RMSE between model predictions and observations for Deuterium and 18 O at the stem base as well as for the water uptake index r U (see 2. 3). Withŷ i as the i th of a total of n observations and y i as the respective simulated value, the RMSE was computed according to: Next, we evaluated the model for 500 random parameter sets within the value ranges given in Table 2. The soil related model parameters were assumed to be identical over the whole profile depth. Based on the observed soil moisture time series we set the volumetric soil moisture at saturation θ s to a fix value of 45%. Since soil moisture levels near saturation only occurred for a short time during the irrigation, we set the model parameter θ c2 to a value of 100%.
Eventually, to relate modelled RWU to our observed xylem isotopic signatures at stem heights of 0.1 and 8 m, we optimized 350 FPLDs that can be described by the following parametric distribution: with F being the probability density function of the Fisher-Snedecor distribution. the second parameter of F was set to a fixed value of 100, so that its first parameter α acts as shape parameter while the additional parameters β and γ act scale and lag parameters, respectively.

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Apart from simply predicting the transformation of δ RWU during its transmission through a tree's xylem, the fitted FPLDs were also used to infer time variable xylem water age distributions. This was achieved by applying the approach described in water). In contrast to the two mentioned studies, the water ages in this study refer to the time of tree water uptake, instead of the time of input as precipitation into the system.

Soil moisture and sap flow
The temporal dynamics of daily sap flow velocities and soil moisture (averaged across the two profiles on the irrigated plot) are 365 depicted in Fig. 4a  From 1 June to 10 June, the first dry period occurred, with soil moisture in the topsoil decreasing towards 15 Vol%. Several rain events between 10 June and 15 June rewetted the soil, but afterwards the soil moisture in all depths declined considerably.

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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. 2.3 established a solid relationship (R 2 of 0.85) between v sap and VPD (see Fig. A4a). Since there are no systematic discrepancies between measured and VPD-derived v sap values (see Fig. A4a), we have high confidence in assuming that the observed periods of reduced v sap during June and July (see Fig. 4a) can be attributed to temporarily lowered VPD 375 instead of soil water deficits.

Stable water isotopes
In each measurement sequence 15 probes (2 standards, 6 SWIPs and 7 XWIPs) were measured within 3 to 5 hours, resulting in one measurement every 12 to 20 minutes. The raw aggregated measurements and the correction procedure are described in Appendices A1 and A2. Some short term fluctuations in the high frequency data caused by diel air temperature fluctuations 380 could be observed that could not completely be removed by the postprocessing procedures. Due to the large amount 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 δ 18 O bias, which was corrected as described in Appendix A2.2. A comparison of the probe heads right after removal from the stem (12 weeks after installation) revealed that 385 the membrane heads of two δ 18 O biased probes were covered by biofilms while an unbiased probe did not show such a biofilm (see Fig. A6).
Focusing on the first period, between 21 May (date of the irrigation) and 10 June, the soil δD-signature was rather stable, while δ xyl increase for 6 to 14 days to reach a plateau. The δD signatures at the stem base at 10cm height (green triangles in We observed two periods 23 June to 11 July and 16 July to 26 July that are characterized by declining soil moisture and rather constant δ soil . Both of these periods show the same pattern of δ xyl 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 July and 27 July) that lead to a replenishment of soil moisture without considerable changes in δ soil . In both cases, we 405 could see an opposite response to the dry period. δ xyl 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 were exhausted within the following days and soil moisture (and δ 18 O signatures) quickly returned the 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 occur again within the observed time period.

Optimization of the RWU model
The temporally and spatially continuous soil moisture and soil water isotope data needed for the optimization of the RWU model was obtained by interpolation of soil sensor data, soil core measurements and SWIP measurements (see Fig. A5).
Subsequently, the optimization was carried out as described in Sec. 2.3.1. Figure  When only the first half of the observational record is considered (darker blue squares and lines), both isotopes show a 420 parameter optimum for z r (rooting depth parameter) between 0.75 m and 1 m (see Fig. 5(d&h)). For that period, it was not possible to identify the optimal parameter value for the other two (water stress related) RWU parameters θ w and θ c1 , which seemed to be rather insensitive to both isotopes (see dark blue squares in Fig. 5(e,f,i&j)).
The maximum lateral root extent r max is critical to reproduce the rise of the Deuterium signal after the irrigation and showed a clear optimum around 3 m (Fig. 5k). The lateral root density decay parameter λ proved to be unidentifiable and was omitted 425 in Fig. 5. When the full time period was considered (light blue diamonds and lines), the optimal values for z r were found at deeper depths between 0.9 and 1.5 m (see 5(d&h)). The optimal wilting point soil moisture θ w ranges between 6-8 % and 7-9 % (for δ 18 O and δD, respectively, see Fig.5(e & i)). Once again, optimal values for r max are at around 3 m, this time for both isotopes.
Unlike of the two water isotopes, the water uptake ratio r RWU relies on soil moisture data alone and is not involved in the 430 convolution step. Consequently, r max was completely insensitive to r RWU . With respect to r RWU , optimal z r values are found between 80 and 100 cm, which is in good agreement with the isotope based z r values in the start phase of the observational record. Based on r RWU , the optimal θ w values are between 7 and 9 % (see Fig.5m) and the optimal θ c1 values are between 30 and 100 % (see Fig. 5n).

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Based on the optimized RWU model, we could compare modelled δ RWU to measured δ xyl values. Except for the Deuterium signatures towards the end of the Experiment, there was a good agreement for both isotopes (see Fig. 6). However, in cases of abrupt δ RWU changes, the observed δ xyl values did respond with a delay which increased with stem height. This was most obvious after the Deuterium-labelling (box A in Fig. 6b). 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 modelled δ RWU values into δ xyl values. which was lower at the start of the depicted period and higher towards its end. Figure 7(b) depicts the same data as Fig. 7(a), but plots their rate of change instead of their absolute values. The colored lines in Fig. 7(a&b) are the results of convolutions of the modelled δ RWU signature with different FPLDs (depicted in Fig. 7(c).

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In order to transform δ RWU into δ xyl.R , we convolved it with two different transfer functions: (1) the conceptually grounded h R (thin green line, defined in Sec. 2.1.2), whose parameters were optimized together with the RWU model parameters and (2) the empirically, more flexible h F1 (thick green line, defined in Eq. 22), whose parameters were optimized subsequently to reach the best possible fit to observed δ xyl.R values. The overall shapes of h R and h F1 turned out to be similar, but the latter achieved a much better fit to the available δ xyl.R observations, while the former failed to adequately reproduce the right-skewed, tailed 450 shape required to fit the observational data (see Fig. 7(b)).
Following this, we simulated the signal transformation of δ xyl.R (at the stem base, thick green line) into δ xyl.H (at 8 m stem height, thick pink line) by convolving δ xyl.R with another transfer function, h F2 (dashed pink line in Fig. 7(c)), whose parameters were optimized to reach the best possible fit to observed δ xyl.H values. In contrast to h F1 , h F2 features a notable time lag around 1.4 m at the beginning and has a strong peak. It's tailing is similar to that of h F1 .

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To directly transform δ RWU into δ xyl.H , it can be convolved with h F1F2 , which is the convolution of the two FPLDs h F1 (root tips to stem base) and h F2 (stem base to 8 m stem height).
than v δ (transport velocity inferred from isotopic tracer observations). Based on our observations, we can infer v δ between the stem base and 8 m stem height to be about 5.5 times faster than v sap .

Xylem water age distributions
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. h F1 and h F1F2 as determined 465 within the previous section, and (2)    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 490 ecohydrological investigations. It contains many of the elements of the "ideal system" sketched by Beyer et al. (2020). To summarize, we list the main advantages of the use of WIPs compared to other in-situ measurement techniques: 1. 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 Rothfuss et al. (2013), Oerter and Bowen (2017) and Kübert et al. (2020), 495 is much more invasive and will inevitably disturb the observed soil to a higher degree. Marshall et al. (2020) relies on boreholes that go all the way through the tree stem.

The borehole equilibration method by
Consequently, with increasing stem diameters, the measurements of this method will increasingly be influenced by the isotopic signature of immobile water from the heartwood. Possibly up to a point where the dynamics of the mobile water transported in the outer parts of the xylem gets hard to detect. WIPs on the other hand are always probing the outer 5 cm 500 of the stem xylem -the same depth as measured with many sap flow sensors.
3. By directly diluting the sample gas within the WIP's mixing chamber, condensation within the sample line is avoided without the need for additional heating of the whole sample line. Additionally, there is an easy way to test the airtightness of the measurement system, by checking how dry a highly diluted sample gets -if it remains moist at maximum dilution rate, there must be some source of moisture (i.e. condensed droplets) between mixing chamber and analyser or other 505 leaks.
4. The identical design of WIPs in soil and xylem, provides a consistent measurement method for soil and tree xylem. This can be considered as an advantage compared to in-situ methods that are only suited for soil (Rothfuss et al., 2013) or xylem . The use of one single type of probe simplifies automating the measurement procedure and interpreting the obtained measurements. reported. Since not all XWIPs exposed such a δ 18 O-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. A6). However, even when the δ 18 O measurements seemed biased, they exposed similar temporal dynamics as unbiased measurements and all of those dynamics agreed with what our proposed modelling framework predicted. So even though we may not be completely sure how to reliably rule out 515 the formation of δ 18 O-bias inducing biofilms, 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 is always possible.
Considering the expected spatial heterogeneity of a skeleton rich, clayey soil -on top of the spatial heterogeneity of infiltration patterns within forest stands (Goldsmith et al., 2019) -and the relatively slow temporal dynamics of the observed soil isotopic signatures, future investigations might benefit using an increased number of WIP soil profiles at the cost of a lower temporal resolution of soil isotope measurements.

Standards and calibration
Our standard probes were sampling the vapour 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 525 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, Gaj et al. (2017) have shown that clay minerals may lead to isotopic fractionation when a label water is applied to oven dried clay rich soils. This might lead 530 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' vapour concentration and isotopic composition (see Fig. A2). As long as the air entering our probes is vapour saturated (which we assume to be the case within transpiring trees and not overly dry soils), the sample gas vapour content is directly related to the temperature of the sampling location. Therefore, we ended up with a 535 calibration procedure that uses the sample gas vapour 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 artefacts of insufficiently compensated temperature effects. A calibration procedure that explicitly considers observed temperatures at 540 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 extends (see (Derby and Gates, 1966)). Even for laboratory conditions, Rothfuss et al. (2013) reported a mismatch between their measurements and the Majoube (1971) equation to compute the isotopic fractionation 545 between the liquid and the vapour phase under equilibrium conditions as a function of temperature.

Process based RWU modelling
We were able to identify meaningful parameters (z r , θ w and r max ) for our process-based RWU model. This model in turn was suited to predict δ RWU . 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 Consequently, the critical model parameters θ w (wilting point) and θ c1 (onset of uptake reduction) were not identifiable (θ w was insensitive when optimized against isotope data, but 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 555 systematically predicts more enriched δ RWU values than we could measure at δ xyl . Since all of the measured soil δD values during that period were more enriched than the observed δ xyl , this is not a failure of the model itself, but rather a consequence of insufficient model input data. This could hint to 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 day measurement interruption in July. While it is nearly impossible to monitor v δ with a high temporal resolution, v sap can be used as a proxy for v δ .

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Previous experiments have shown that v δ may exceed v sap by several hundred percent. Meinzer et al. (2006) reported v δ to be five times higher than v sap and Schwendenmann et al. (2010) even reported it to be about 16 times higher than v sap . This can be explained by the fact that not all of the xylem area probed for v sap measurements is actively contributing to sap transport.
Unaccounted wounding errors from the probe installation may lead to additional underestimations of v sap . Irrespective of a possible systematic scaling error, Meinzer et al. (2006) reported a good correlation between v sap measurements v δ values. We 570 also observed a mismatch between v sap and v δ : h F2 , the optimized FPLD between 0.1 m and 8 m height, featured a lag of only 1.43 m (in the sap distance domain based on v sap ), which indicates, that the actual FPLDs are likely 5.5 times longer than our apparent, v sap based FPLDs shown in Fig. 7(c). However, this scaling error is of no consequence as long as the apparent FPLDs are not interpreted directly, but simply used to predict tracer time series.
Our conceptually derived h R , which was based on assumed vertical and lateral root distributions, proved suited to act as 575 FPLD between δ RWU and δ xyl.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 r max via model parameter optimization, where r max was identifiable when the model was evaluated with respect to δ xyl.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 r max estimate greatly improves with a distinct artificial isotopic labeling pulse.

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However, the overall shape of the conceptually derived h R was unable to fully reproduce the skewness and tailing of the fitted parametric distribution h F1 (from Eq. 22), 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 be caused by dispersion during the the root xylem passage, as we see a similar tailing for the transport along the stem (represented by h F2 ). Future labeling experiments with sequentially applied tracer pulses limited to certain radial distances from the stems of trees with different 585 characteristics could help to study macroscopic and microscopic factors that shape the FPLD of a tree's root xylem.

Xylem water ages, FPLDs and their implications
During the main growing season 50% of all xylem water passing the stem base of our studied beech trees was older than 1.6 days. When looking at the 8 m stem height, the mean median xylem water age was 4.7 days. Assuming the xylem water transport velocities are not changing fundamentally above that point, we can estimate that the mean median water age of the 590 xylem water within the tree crowns of our studied trees was close to 10 days. 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 labelling, but also during periods where water stress may lead to changes in δ RWU .
Previous studies (James et al., 2003;Meinzer et al., 2006;Schwendenmann et al., 2010;Gaines et al., 2016) have typically 595 investigated above ground 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. Knighton et al. (2020) citing the study of Gaines et al. (2016), claimed they had "estimated time lags between RWU and 600 transpiration", while they actually had estimated time lags between tracer injection to the stem base and transpiration. Similarly, de Deurwaerder et al. (2020) propose a modelling framework that erroneously equates δ RWU to δ xyl at the stem base, leading them to the prediction of unlikely clear δ xyl signals further up the stem. The FPLD between root tips and stem base (h F1 in Fig.   7(c)) contributes considerably to the smoothing of δ RWU , much more than the FPLD along the first 8 m stem height (h F2 in Fig. 7(c)). Consequently, we strongly suggest to include the below ground fraction of the tree into any endeavour that aims to 605 simulate the propagation of δ RWU 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 610 vertical and lateral root distributions can be achieved by convolution of δ RWU with an appropriately shaped FPLD.

Conclusions
This study demonstrated the application of a measurement setup which facilitates unprecedented high frequency monitoring of stable water isotopes in soil and tree stem xylem. We were able to predict the observed time series of xylem water isotopic concentrations at different stem heights with a combination of a process based RWU model and a convolution based approach 615 that accounts for the FPLD between root tips and the sampling points in the tree stem.
Our results showed, that δ RWU and δ xyl are often similar but not necessarily the same. No δ xyl measurement can represent actual δ RWU : it will always be an integration over certain fractions of δ RWU from different points in the past. Therefore, we have to reject our first hypothesis, that a tree's xylem water isotopic signature is equivalent to the isotopic signature of RWU.
Only under certain conditions (i.e. little temporal variability of the RWU composition or short transport distances combined with high xylem water transport velocities) can FPLDs within the plant safely be neglected. Otherwise, plant water isotope models should account for the FPLDs between RWU and the sampling point used for model evaluation or between RWU and transpiration in the leaves.
Regarding our second hypothesis, we conclude that a conceptual representation of a tree's root system is capable to reproduce the basic shape of the FPLD between δ RWU and δ xyl . But more detailed observations and experiments are needed before tree 625 root xylem FPLDs can robustly be derived from observable tree characteristics and the tree architecture.
Due to the smoothing effect of FPLDs, sub daily observations of tree xylem water isotopes are unlikely to reveal much information about short term RWU dynamics. Except for precipitation events, soil water isotopes show even smaller temporal dynamics. Consequently, future investigations of stable water isotope dynamics should favour an increased number of probes in soil and xylem to cover spatial heterogeneity over high subdaily measurement frequencies.

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Code and data availability. The supplement to this study contains the processed WIP measurements and all the climate-, sap flow-and soil moisture data needed to reproduce the essential results presented in this article. Furthermore, the supplement contains R-scripts that recreate the 2-D interpolation of soil moisture and isotopes (S1_soilInterpolation.r), the computation of δRWU (S2_XWIPs_and_RWU.r), the time series transformation and convolution of isotopic data (S3_transformation_and_convolution.r) and the computation of xylem water age distributions (S4_xylem_water_age.r).
Appendix A A1 Raw in-situ measurements showed a greater temporal variability resembling diurnal temperature fluctuations, while the thermally better insulated soil probes yielded more constant values over the day. Since the high frequency data seems to be dominated by those temperature related diurnal fluctuations and there are so many data points, we chose to focus on daily median values, which are plotted solid in Fig. A1, while the underlying data points are plotted transparently in the background. On top of Fig. A1 we indicate some incidents that need to be commented on:

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(A) We missed to measure the initial conditions and our first measurement days might have been impaired by moisture within our measurement system that first had to be flushed out over time.
(B) During a rainfall event, stem flow intruded along the shaft of an insufficiently sealed WIP (T1R) diagonally installed into a tree root. After the water had entered the system around early 11 June, subsequent measurements of all other probes were unusable until we managed to visit the field site at June 13 to manually flush all tubing with dry pressurized air. Then we renewed the silicone sealing to protect probe TR1 from further water intrusions. While all other probes were back measuring, probe TR1 needed five more days to return to its normal operation.
(C) During a storm event, some cable connections became loose. Starting with probe T1H, and a few days later continuing with the neighbouring probes T1R and (SWIP) 100 cm. The valves for those three probes did not switch and the CRDS's vacuum pump sucked its sample gas through the least air tight point in our assembly, rendering the respective data useless.

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(D) Some time after changing the gas cylinder holding the dry air at 2 July, a seal failed -emptying the gas cylinder much faster than expected. Due to a holiday leave it was not fixed before 11 July.
(E) Some animal nibbled through the tubing at the shaft of the xylem probe T2R and severed the tubing completely from the probe.

A2.1 H 2 O-ppmV correction
Following the volumetric moisture correction procedure described in section 2.3, the relationship between volumetric sample moisture and the raw vapor δ 18 O and δD for both standards are shown in Fig. A2(a & b), respectively. We split the whole data notable spread of slopes, it turned out that the differences between the utilization of one (overall mean) slope for the moisture correction over the whole experiment does not lead to big differences compared to the utilization of period specific slopes.

A2.2 Manual data corrections
In terms of δ 18 O, three XWIPs (T1B, T2B and specifically T3B) exhibited similar dynamics in their time series compared to the remaining XWIPs (T1R, T1H, T2R and T2H), but seemed to have a negative offset, without any corresponding offset in  qq q qq q q q q q qq qq q q qq q qqq q q q q q qqqq q qqq qq q q q q q qqq qqq q q q q qq q qqqqqqqqq q q q q q q q q qq qq q q q q qqq q qq qq qq q qqq qq q qq qq q q qq qq q q qqq q q q qq q q q qqqq qq qq q qqqqqqqqqqq q q q q q q qqq q q q qq q q q q q q qq qqqq qqq q qqqq q q qq q qqq q q q qqqq q q qq qq qqqqq qq qq qq qqq qq qqqq q qq q q q q qq qq q q qq q qq q q q qq q q q qq qqq q qqq q qqqq q qq q q qq q q q q qqqqq qqq q q qq q q q q q q qqqq q q q q qq q q qq q q q q qq qq q q q q q q qq qqq q q q qq q q qq q qq qq q q q q q qq q q q q q qq q q q qqqq q q qq qq qqqq q q q qq qq q q q q q qq q q q q q qqq q q qq q qq q q q qq q qqqq q qq qq qq q q q q qq q q q qq q qq q q q qqq q qq q qqqq qqqq qq q q q qqqq q qq qq qq qq q qq q qq q q q q q qqq q q q q q q q q q q q q qq q q q qqqqqq q qq q q qqq q qqq q qqq q q q qqqq q q qq qq qqqq q q q qq qqq q q qq q qqq qqqq q q q qq q q qq q qqqq q qqqqq q q q q q qqq qqqqqq q qq q q q q qqq qqq qq qqq q q qq q q q qqq qqqqq q q q qq qq q q q q q qq q q q q q qqqq q qqqqq q q q qqqqq qqqq q q q qq qq q q q qq qq q q q q q qq q qq qqqqqq qq qqqq q q qqqqqq q q q qq q q q q q qqq q q q qqqqq q q q q q qq q q qq qq q qq q q q qq qq qq qq q q qq qq qq q q q q q q q qqq qq q q q q q q q q q qqqq q q qq q qqqq qq q qqq qq qqq qqqq qqq q q q q q q q q q q qq qqqqqq q q q qq q qq qq qq qqqq q q q qqq q q q q q q qq q q q q qqq qq qq qqqqqq qqq q q qq q q q q q q q   M a y -2 1 J u n -0 1 J u n -1 1 J u n -2 1 J u l-0 1 J u l-1 1 J u l-2 1 A u g -0 1 A u g -0 8 irrigation (c)   10cm  20cm  40cm  60cm  80cm  100cm  T1R  T2R  T1B  T2B  T3B  T1H  T2H (  ) 10cm  20cm  40cm  60cm  80cm  100cm   XWIPs   T1R  T2R  T1B  T2B  T3B  T1H  T2H Bulk rainfall Initial soil cores