The isotopic composition of the net exchange flux (δET or δNEE) is comparable to the source isotopic composition being mixed into a reservoir. The difference is that δET and δNEE can also describe the composition of a negative (uptake) flux. The common approach for determining the isotopic composition of a source from atmospheric measurements are mixing models, as described by and . In these models, changes in atmospheric isotopic compositions are directly related to changes in mole fractions. For example, when increased mole fractions are associated with enriched isotopic compositions, the source is understood to be more enriched than the atmospheric background. In the Miller-Tans (MT) method, the slope of the relationship between δχ and χ is solved for to find the isotopic composition of the source (example in Appendix Fig. ). In various studies, the MT method has been used to determine δET or δNEE irrespective of the flux sign . We refer to estimates using the MT methods with δ…,MT.

The isotopic composition of the net turbulent exchange flux can also be estimated with measurements of the turbulent exchange fluxes of the various isotopologues of the target species . δ fluxes (Fδ) provide a common method to determine such an isotopologue flux. 3Fδ=w′δ′‾ where, w′ and δ′ are the fluctuating components of the vertical wind and isotopic composition, respectively, after Reynolds decomposition . Fδ has the units ‰ m s⁻¹. For the example of δD in water, FδD is related to the isotopic composition of the net flux (δDET), the atmospheric isotopic composition (δDatm), and the total exchange flux (in this case ET) as follows . 4FδD=ETρvatm⋅(δDET,F-δDatm) Here, ET is the evapotranspiration flux in gm-2s-1. ρvatm is the atmospheric absolute humidity in gm-3, and δD_atm is the atmospheric isotopic composition of deuterium in water vapour. Note that the fraction ETρvatm defines an exchange rate. The unit grams in the nominator and denominator can thus be replaced by moles. The isotopic composition of the net exchange flux (δDET), determined using this flux method (δ…,F), can be solved for and inserted into Eq. ().

Until recently, the δ flux (Fδ) could only be inferred by relating gradient measurements of isotopologues to an exchange coefficient depending on mechanical and convective turbulence . At present, high flow rate laser spectrometers are available which measure the isotopic composition at sub-second frequencies, which allow for direct isotopologue flux measurements using the eddy covariance technique . The difficultly in using such measurements is keeping the instrument stable, while maintaining high flow rates and an undisturbed inlet gas stream, which is necessary to resolve both the longest and shortest turbulent exchange timescales . We found that temperature-stabilized enclosures, combined with short, heated inlet lines provide a workable mode of adhering to these constraints (see Sect. ).

In this work, we focus on the δ18O isotopic state or isotopic cascade of CO₂ in the relevant reservoirs of the ecosystem, and on the isotopic link between CO₂ and H₂O. Our measurements also include δ13C and we show the time series of δ13C fluxes in Sect. , but do not investigate δ13C in the individual reservoirs. The reason for this is that δ13C has been thoroughly investigated to constrain the exchange of CO₂ on various scales . On global scales it has proven to be a highly valuable tracer for separating oceanic, fossil, and biospheric sources and sinks . At ecosystem scales however, the small isotopic disequilibrium between photosynthesis (P) and respiration (R) has been limiting for acquiring reliable partitioning results . The combined water and CO₂ isotopologue flux measurements performed during CloudRoots-Amazon22 provide a unique opportunity to explore the ecosystem flux partitioning using the δ18O-CO₂ cycle instead.

Besides describing a representative diurnal cycle, we describe the isotopic state of the entire ecosystem in depth at 14:00. Our reason to select this period, is that fluxes are largest, the boundary layer has fully developed and the vegetation has reached isotopic steady state . Here we use additional isotopic information from leaf and soil samples collected from 12 to 15 August 2022, which are described in . For the leaves, samples taken from the canopy top (30 m) or the middle of the canopy between 12:00 and 16:00, were averaged to represent the 14:00 isotopic state. Soil samples were assumed not to vary in isotopic composition during the day. Here, the topsoil represents depths between 0–10 cm, and the deep soil depths between 40–100 cm. The isotopic composition of xylem water (δxyl) was approximated as the average of deep soil samples (40–100 cm depth, −3.83 ‰ for δ18O) and a water sample collected from a stream at approximately 70 m lower elevation (-4.86 ‰ for δ18O) which drains the plateau that hosts the ATTO site (see Fig. ).

Averaged afternoon profile data of wind speed, relative humidity, CO₂ mole fractions, and temperature were used to accurately describe the environmental conditions near the leaves and the soil . Soil temperatures were measured at three locations, and the averaged 14:00 temperature was used for our analysis.

Finally, measurements of atmospheric δ18O-CO₂ compositions from flask samples were incorporated. In total, the data from 22 flasks were used to determine a representative 14:00 value. These were collected from air sampling inlets on the ATTO tower ranging from 50 to 312 m and collected during the early afternoon (12:00 and 16:00) on 14 and 15 August 2022. The data from the CO₂ isotope analyser could not be used to determine the background isotopic composition as it had a temperature dependent instability.

For the atmospheric compositions, δ fluxes, and ecosystem source compositions, the uncertainty associated with the 14:00 values represent the variability over the 13 composite days, expressed as the standard deviation (SD). In the case of leaf and soil samples, the uncertainty is the standard error of the mean (sem) of the samples. The uncertainty in δR is determined by propagating the sem in the topsoil water samples. For δP, we instead based its error on its sensitivity to ci/ca, where we assume that the ecosystem wide ci/ca was determined with a 0.01 error (see Fig.).

Fig.  shows the composite diurnal cycle of the 57 m H₂O flux. We find a strong evapotranspiration flux during daytime, matching the period of solar irradiation (sunrise: 06:04, sunset: 18:04). Nighttime fluxes were close to zero, reflecting the reduction in turbulent transport and lack of available energy for evapotranspiration. The magnitude of the uncorrected H₂O flux derived using the water isotope analyser was 9.9 % smaller compared to the one derived with the conventional Open Path Gas Analyser (OPGA). Previously, water isotopologue flux studies have reported differences of tens of percent, indicating that we captured the high frequency contributions to the turbulent exchange flux reasonably well .

The diurnal cycles of the δ fluxes have a very similar shape compared to the evapotranspiration flux. The variability over the days was somewhat larger however for the δ fluxes, as shown by the 25 % and 75 % quantiles (shaded). We applied the spectral correction method described in to compensate for possible high frequency signal loss. Here, the cospectral power of frequencies lower than 8×10-2 Hz were used to estimate the cospectral power of the highest frequencies contributing to the flux. The black dotted line in the bottom two panels indicates the impact of this correction.

For δD, the magnitudes of the fluxes with and without spectral correction are effectively equal, indicating small high frequency signal attenuation. This finding was confirmed by the w′-H2O′ co-spectra related to the H₂O flux (see ). For δ18O, the spectral correction added 15.5 % to the flux, suggesting that there was a loss of high frequency signal for H218O. As attenuation is generally comparable for the various H₂O isotopologues, this was unexpected. Investigating the cospectra revealed that for δ18O, most frequencies contributed to the positive isotopologue flux as expected, but the highest frequency eddies had negative contributions (see Fig. ). The reason for this phenomenon could not be identified.

Figure  shows the composite day overview of the isotopic composition of the net ET flux (δET) derived using the Miller-Tans (δET,MT) and Flux (δET,F) methods. For δ18O as well as for δD, we find that δET is always enriched compared to δatm. During nighttime, the isotopic composition of the net flux is highly variable over time for both species. For the flux method, this is directly related to the very small (near-zero) water vapour and δ fluxes shown in Fig. . Equation () clarifies that a large uncertainty for the fluxes leads to poor estimates for δET,F. For the Miller-Tans method, the small perturbations in isotopic compositions and mole fractions associated with stable nighttime conditions also lead to large uncertain δET,MT estimates. Moreover, these stable conditions suppress mixing, which leads to horizontally heterogeneous conditions in the forest, which results in variability between the different nights . During daytime, the isotopic compositions of the net exchange are instead well defined, with little variability between the contributing days.

From 10:00 to 17:00 we find that δET is quite constant, with a 40 ‰ enrichment for δD, and a 5 ‰ enrichment in δ18O compared to the ambient atmospheric water vapour. This is consistent with the evapotranspiration of comparatively enriched water from the ecosystem to the atmosphere. For both δ18O and δD we observe that net flux compositions obtained with the flux method (δET,F) are more enriched than those derived from the Miller-Tans method (δET,MT) during the same period. On average, the difference is 6.4 ‰ for δD and 1.9 ‰ for δ18O. The causes of this difference and the implications for the partitioning of ET are discussed in Sect. .

In Fig. , the CO₂ flux and corresponding isotopologue flux measurements are summarised. The NEE flux in the top panel indicates strong negative CO₂ flux during daytime, indicating photosynthetic uptake. Immediately after sunrise, however, a small positive CO₂ was observed. We interpret this positive flux to be related to the nighttime respiratory flux, which feeds CO₂ into the nocturnal boundary layer . As this layer is stably stratified due to the radiative cooling of the surface, the CO₂ is trapped in the atmospheric layer below the 57 m measurement height, which includes the entire canopy. When the stability is broken after sunrise, this accumulated respiratory CO₂ is transported upward to the boundary layer and across the measurement location.

The fluxes derived with the closed path CO₂ isotope analyser compare very well to the OPGA, without any notable signal loss. The δ fluxes can thus also be expected to be resolved well. In terms of diurnal pattern, the δ flux of δ13C is a mirror image of the NEE flux, including the release of trapped nocturnal respiration after sunrise. During nighttime, both the ¹³C δ flux and NEE show a near continuous respiration flux, which is unlike the near zero fluxes for ET and δ18O-CO₂.

The ¹⁸O-CO₂ δ flux has a diurnal pattern which is more similar to the ET and water isotope δ fluxes. The main difference is the time from which the flux becomes positive, which is delayed by 1.5 h for ¹⁸O-CO₂. The effect of the spectral corrections is similar for both δ13C and δ18O, although somewhat stronger for δ18O. Here, the method described in was primarily used to correct for instrument instabilities at frequencies lower than 9×10-4 Hz. Since the instrument instability increased the variability of the isotopic signals, and thus increased the magnitude of the flux, the spectral correction method leads to smaller δ fluxes for CO₂.

Figure  shows the composite day overview of the isotopic composition of the NEE flux (δNEE) derived using the flux (δNEE,F) method. While for H₂O the source composition can be interpreted as the composition being mixed into the atmosphere, this is not as self evident for CO₂. This is because the net exchange of CO₂ transitions from positive values during nighttime (R) to negative values during daytime (P and R). Following Eq. (), the isotopic composition of the net ecosystem exchange flux must be interpreted in line with the sign of the flux. Thus, during daytime it represents the isotopic composition of the (negative) uptake flux. For δ13C, we find uptake flux compositions which are depleted by 20 ‰ compared to the atmosphere during both day and nighttime (see Fig. ). At nighttime, this represents the signature of respiration from decomposing organic matter. During daytime, the isotopic signature of the assimilated CO₂ is measured, which reflects the preferential uptake of depleted carbon by C3 vegetation (trees). Note that during daytime, contributions from the depleted respiration flux are also present.

The ¹⁸O isotopic composition of the NEE is approximately -15‰ lower than the one of ambient atmospheric CO₂ during the night according to the bottom panel of Fig. , and this difference steadily increases to -50 ‰ in the late afternoon. As explained above, this is an apparent fractionation that does not represent the fractionation associated with physical CO₂ uptake, but it is due to back diffusion of CO₂ after isotopic exchange with water. Thus, it is necessary to consider the δ18O of the water with which CO₂ equilibrates in the leaves. During nighttime, leaf water is strongly depleted in δ18O compared to daytime, which leads to respired CO₂ being depleted in δ18O compared to atmospheric CO₂ (see Table ). This δ18O depletion is indeed observed at night. During daytime, δ18O in leaves gradually increases due to evaporative enrichment. As a consequence, the CO₂ molecules that exchange isotopes with water and are partially assimilated must also be comparatively enriched in ¹⁸O.

So, why do we then observe a continuous depletion in δ18O_NEE compared to the atmospheric δ18O value? This is due to the net uptake of CO₂ during daytime (negative CO₂ flux), combined with the substantial diffusion of equilibrated and thus isotopically enriched CO₂ back into the atmosphere . The latter effect is dominantly responsible for affecting the atmospheric isotopic composition of CO₂. However the (apparent) composition of the net uptake flux is what is determined. In our case, this net uptake flux seemingly strongly favours ¹⁶O, as it enriches the atmosphere in ¹⁸O, which results in a negative δF18O . The strongly depleted δ18O composition of the daytime carbon flux is thus a consequence of the enrichment of the atmosphere due to back-diffusion. Other researchers have found similar diurnal cycles for δ18O to the ones we present in the bottom panel of Fig.  (for example , their Fig. 9b (dry conditions)). The apparent fractionation effect during photosynthetic uptake is further explored in Sect. .

During the transition to nighttime respiration, leaf water remains temporarily enriched in ¹⁸O, which leads to the enriched source signature visible between 17:30 and 20:00. Here, the NEE and δ flux are near zero, leading to more variability between the days, as indicated by the shaded area. Compared to the highly variable nighttime source compositions for H₂O, the source compositions for the CO₂ isotopes are better defined during the night. This is because there are still significant net exchange fluxes and isotopologue fluxes during nighttime. During the morning, the transition between the respiration peak and the onset of photosynthesis is more abrupt than during the evening transition, which allows for the source compositions to be well estimated comparatively during that time. During the evening transition around 18:00, when the sign of the net exchange flux changes to the respiration dominant nighttime, some erratic NEE isotopic signatures are also found in ¹³C.

We investigated the isotopic signatures of H₂O in water reservoirs that are relevant for the exchange of water (and CO₂) around the ATTO tower. Here, we describe the isotopic compositions within the soil, canopy, and atmospheric reservoirs, as well as the isotopic composition of the associated vertical water vapour flux as measured above the canopy. The isotopic compositions of reservoirs which were not measured directly and of individual gross fluxes were then derived following Sect. . The result is a coherent and connected isotopic cascade throughout the Amazonian ecosystem. We describe the 14:00 case which ensures that the atmospheric boundary layer (ABL) is fully developed and that isotopic steady-state has set in. To limit the effect of the sub-diurnal and inter-diurnal variability, the 14:00 case was derived from a 13 d composite diurnal cycle.

Table  specifies the typical environmental conditions at 14:00 at the ATTO site. These variables are key inputs for describing the isotopic H₂O and CO₂ balances. For a rainforest, the RH of 58 % within the canopy is relatively low. Note that the campaign took place during the dry season, and that only two significant rain events took place during the 13 d campaign. In addition, temperatures are highest around 14:00, contributing to a reduced RH. As a consequence, the vegetation limits evaporation by reducing its stomatal apertures, resulting in a comparatively high stomatal resistance Rs during this time. In line with this, the ci/ca is at a daily low at 14:00.

The right hand side of Fig.  specifies the isotopic state of water in all the relevant reservoirs for both δD and δ18O. Here, we combined atmospheric observations, flux measurements, and leaf and soil level measurements (also see Table ). Two flux pathways are highlighted by which water vapour is fed to the atmosphere: (soil) evaporation and transpiration, respectively. Here, the transpired water (δT) is enriched compared to the atmospheric reservoir (δatm), whereas the evaporated water δE is depleted compared to δatm. This difference is key to resolve, as it allows us to partition the net ET flux into the components E and T in Sect. .

Ultimately, the source water of both evaporation and transpiration is the same, namely precipitation. While there is some seasonal variability in the isotopic composition of precipitation, with the wet season feeding more depleted water to the ecosystem, this will not impact our 13 d measurement campaign . The isotopic composition of topsoil water (δsoil) is determined by the composition of recent precipitation and the accumulated effect of the evaporative enrichment of the near-surface water reservoir due to Rayleigh fractionation. The latter effect results in the topsoil water to be more enriched compared to the water below (see Fig. ). Compared to δsoil, the evaporated water δE is strongly depleted due to the preferential evaporation of HHO compared to HDO .

As explained above, the isotopic composition of transpiration (δT) is assumed to be identical to δxylem because of mass conservation . As a result, the isotopic composition of transpired water vapour (δT) is much more enriched than δE. The Craig-Gordon model (Eq. ) allows to determine the isotopic composition of liquid water at the exchange site (δe) that is required to supply these high values of δT. The results representing our study case are shown in Fig. : δ18O_e is 15 ‰ higher than δ18O_xylem, while δD_e is more than 50‰ more enriched than δD_xylem. Liquid water samples of entire leaves (δL), which comprise both the leaf veins and the leaf lamina, bridge the composition of the enriched evaporation sites, and the comparatively depleted δxylem source water . Given that we know both of these end members, and the leaf water isotopic composition, we are able to estimate a value for the Péclet number using Eq. (). Since we also know the transpiration rate from the partitioning result, we can subsequently solve for L in Eq. (), which is the effective path length over which water transport in leaves takes place. This results in a value of L=10 mm, should be seen as a representative value for the entire footprint of the EC system, and accounts for transport through both the larger leaf veins and the smaller leaf capillaries. This value for L was associated with Péclet numbers of 0.61 for δ18O, and 0.6 for δD. Table  specifies the important intermediate steps in the isotopic cascade, and also provides the uncertainties for some of the variables.

The left hand side of Fig.  specifies the 13 d averaged 14:00 isotopic state for δ18O-CO₂. Similar to H₂O, two flux pathways are highlighted which together determine NEE, namely the (soil) respiration flux (R) and the photosynthetic assimilation flux (P). Importantly, the isotopic exchange of ¹⁸O-CO₂ is controlled by the isotopic composition of H₂O throughout the ecosystem, which means that tight links between the left and right hand sides of Fig.  exist.

The isotopic composition of assimilated CO₂ (δP) is apparently strongly depleted in ¹⁸O compared to δatm. This is a particularly important and counter-intuitive effect in the δ18O-CO₂ cascade, and it results from the isotopic exchange between CO₂ and H₂O in the mesophyll of leaves. Oxygen isotopes are exchanged so quickly between CO₂ and H₂O that the isotopic composition of CO₂ in the stomata is generally believed to be in isotopic equilibrium with the H₂O at the site of exchange . This means that the δ18O-CO₂ in the stomata is decoupled from the isotopic composition of ambient CO₂, and in our case enriched (see δc). As mentioned above, part of this isotopically enriched CO₂ diffuses back through the stomata and isotopically enriches the atmospheric reservoir. The net effect of the CO₂ exchange through the stomata is (photosynthetic) uptake however, so the atmosphere close to the leaf does have lowered CO₂ mole fractions. The combination of the net uptake and the back-diffusion of ¹⁸O- enriched CO₂ makes it seems as though ¹⁶O-CO₂ is apparently assimilated faster than ¹⁸O-CO₂. It is important to realize that this is not what happens physically, but that an apparent fractionation effect takes place .

δP-δatm indicates the strength of the apparent fractionation effect, which is -35 ‰. This difference is larger than what might be expected given the isotopic composition near the exchange sites (δe) in the mesophyll (δc-δatm) of about 8 ‰. In Sect.  we detail how this amplification emerges in relation to the ci/ca ratio, which determines the relative strength of the back-diffusion. This effect turns out to be key for partitioning NEE. In contrast to δP, the isotopic composition of respired CO₂ (δR) is only weakly depleted relative to δatm (-14.1 ‰).

The source signature of the soil respiration flux (δR) is primarily affected by equilibration with the soil water isotopic composition. Any CO₂ in the soil, whether it has been locally respired or invaded from the atmosphere, equilibrates with topsoil H₂O_l (δsoilliq, ). During the subsequent diffusion from the soil into the atmosphere, the CO₂ from the soil (δsoilCO2) undergoes kinetic fractionation (Table ). This results in a depletion of the isotopic composition of the respiration flux (δR) compared to δsoilCO2. In addition, invasion of CO₂ into the soil and subsequent back diffusion into the atmosphere has a depleting effect. However, as the concentration of CO₂ in a tropical rain forest soil is much higher then in the atmosphere, this effect is comparatively small .

In total, the enriching effect of δP on δatm is larger than the depleting effect of δR, which results in the net positive δ18O-flux we observe in Fig. . In line with this, and given that the NEE flux is negative, the isotopic composition of this flux (δNEE,F) is depleted compared to the atmospheric background. Using our measurements and Eq. (), δNEE,F was determined as -1.6‰. This is lower than both the canopy and the soil flux end-members δP and δR, which can seem illogical. This is, however, a mathematical effect of attributing the depletion associated with both gross fluxes to one, smaller, net flux. In fact, we show below that the derived value of δNEE,F does allow for the flux partitioning equations to be solved (Sect. ), and it is in line with previously measured values by, for example, , who found a δNEE,F of -10.5 ‰ above a soybean field.

The values established in previous sections can be used to partition the measured net ecosystem exchange fluxes NEE for CO₂ and ET for H₂O into the individual gross flux components according to Eq. (). δET was taken as the average of the values determined from the direct flux measurements δET,F and the Miller-Tans mass balance approach δET,MT. δE was assumed to equal δsoilvap, as described in Sect. , and δT was represented by δxyl (see Sect. ). Using the average of the partitioning results derived from δD and δ18O, we find that the transpiration flux (T) contributes 95.5 % to ET at 14:00 on average (Fig. ). A dominant contribution of T is expected given the high uptake of radiation by the canopy crown and resulting shading in the understory . The 4.5 % contribution from soil evaporation flux (E) is an important finding, as few studies have attempted to estimate the soil contributions, and it is assumed in many studies that no soil evaporation takes place at all . Note that ET partitioning using δD only results in E=0, as δD_ET is even more enriched than δD_T according to our measurements.

For the NEE flux, the partitioning suggests that P is 144 % of NEE, which is compensated by an R of -44 % of NEE (Fig. ). We found that this result was strongly dependent on the component δP, which is the apparent isotopic composition of P. Given its origin from CO₂ back-diffusion, the strength of δP depends on ci/ca. For the value we used (ci/ca=0.79) we find δP=7.8 ‰. To interpret δP, it helps to consider ci/ca as describing a balance of opposing diffusive fluxes (Fout/Fin∝ci/ca1-ci/ca). The value of 0.79 means that for every CO₂ molecule being assimilated, roughly 4 CO₂ molecules diffuse back into the atmosphere. This illustrates that while the enriching effect on the atmosphere is not large per back-diffusing molecule (see Fig. ), the effect is leveraged 4 fold when interpreting it as a fractionation effect resulting from photosynthetic uptake alone. In Sect.  we explore the sensitivity of the partitioning result to this uptake fractionation leveraged by ci/ca.

The uncertainty in the partitioning result is determined by the uncertainties in the net ecosystem fluxes (ET and NEE), the isotopic end-members (δE, δT, δR, and δP), and the derived isotopic composition of the net ecosystem exchange fluxes (δET and δNEE). Here, the uncertainties in the isotopic components can be assumed to be largest. In Tables  and  we provide the estimated errors in all of these isotopic components. Note however, that the various types of errors are not directly comparable. For example, the large uncertainties in δET and δNEE, which indicate the variability (SD) in these variables over the 13 composite days, are likely smaller than the end-member compositions (sem) when considering the instantaneous 14:00 afternoon case we analyse (see Sect. ). As a result, we have not explicitly determined uncertainties for the partitioning results.

As shown above, we have used high frequency isotope measurements to determine the isotopic composition of the ecosystem flux (δET and δNEE). For δET, two estimates were used and compared: one using the measured δ flux (δET,F) and the other one using the Miller-Tans δET,MT method. We found that δET,F produced systematically more enriched values, where δD was 6.4 ‰ more enriched and δ18O was 1.9 ‰ more enriched compared to δET,MT. also compared the δET,F to a mixing model method, however for δ13C of CO₂. They found that δET,F was ≈5 ‰ more enriched, which in their case meant closer to δa, than δET,MT. They attributed this systematic effect to footprint differences. δET,F indeed represents local exchange in the footprint area of the isotope and the net ecosystem flux measurements, while δET,MT can also be influenced by other up-wind exchange processes, which affect the measured atmospheric compositions (see Fig. ). It is not clear, however, why up-wind exchange would be much different compared to local exchange, given the homogeneity and vast scale of the Amazon rainforest ecosystem surrounding the ATTO site.

We suggest that differences between δ…,F and δ…,MT should be further investigated to determine which method is more appropriate for determining the isotopic composition of the ecosystem flux. For now, we speculate that the estimate from δ…,F will be more reliable because (1) the footprint better matches the flux and in-ecosystem measurements we took, and (2) because the Miller-Tans method is subject to stringent assumptions which are not underlying the flux method. Here, especially the two end-member mixing assumption is likely violated, as vapour sources from an ecosystem are not isotopically uniform, but highly variable in composition .

Determining flux partitioning at the ecosystem scale is important for linking the understanding of leaf and canopy scale processes to the scales relevant for remote sensing and modelling purposes . It is important to realize that leaf and soil water isotopic composition measurements are always necessary to determine the end members for isotopic partitioning. In addition, ci/ca ratios need to be known, and they are usually determined with dedicated (and labour intensive) leaf gas exchange measurements . While we attempted to capture the variation across space and species in these variables, it is challenging to obtain a subsample that is truly representative for the entire ecosystem. Moreover, such measurements are labour intensive. Once a high temporal resolution isotopologue flux system is in place, this may be the least time consuming component of the flux partitioning system. Therefore, we consider the necessity of detailed leaf and soil scale measurements to be the major obstacle for more wide spread implementation of isotopic ecosystem scale flux partitioning.

Replacing detailed leaf and soil scale measurements with assumptions or approximations based on environmental variables is appealing for simplifying isotopic ecosystem scale flux partitioning. For example, the ci/ca ratio is regularly assumed to be 0.7 . Alternatively, its value can be approximated using the stomatal conductance and the water vapour pressure deficit . However, we find that the isotopic end-member δP is highly sensitive to the ci/ca ratio, which makes us believe that approximations are likely insufficient for deriving reliable partitioning values. Even with the intensive ci/ca monitoring during CloudRoots-Amazon22, described in , we are left with some uncertainty regarding an appropriate ci/ca ratio. Figure  indicates how this uncertainty propagates to the determination of δP, and what the consequences are for the NEE partitioning result.

For our observed value of ci/ca=0.79, Fig.  indicates that an isotopic composition of the canopy uptake flux (δP) is found which allows for the partitioning of NEE. However, the upper bound of the possible ci/ca range would result in a δP close to the solid horizontal line, which indicates the limit of possible partitioning results, leading to a respiration flux of near zero. The lower bound of the possible ci/ca range, 0.77, which is only smaller by 0.05, would instead suggest a large R (-69 % of NEE), compensated by a strong P uptake flux (169 %). The exact value of the ecosystem wide ci/ca is thus important to know. Note that the daytime averaged ci/ca is approximately 0.86, which does not allow for partitioning at all. To describe the ecosystem exchange, it is thus essential to resolve the diurnal cycle of variables like ci/ca with measurements, which allows for the diurnal dynamics to be taken into account appropriately.

For the H₂O isotopes, the assumption of isotopic steady-state is important and much discussed . This assumption emerges from the principle of mass conservation, and implies that during continuous transpiration, a balance is established between the isotopic composition of the water taken up by a plant, and the water vapour transpiring into the atmosphere. This directly relates to the strong isotopic enrichment of the water at the evaporation sites in the leaves, which leads to and maintains the enrichment of the transpiration (vapour) flux. While this assumption is adequate for longer timescale (1 month) analysis, it has been shown to be problematic at short timescales (<1 d), where irregularities due to buffering and fast fluctuations in environmental conditions are observed . In our analysis we have used the steady-state Craig-Gordon model. For the 14:00 case, we do not expect the steady-state assumption to be violated, as this is the time of day where enough water has been processed through the plant, and is being transpired, for steady-state to set in . However, if we expanded our analysis to the entire diurnal cycle – where during the night transpiration is small and the leaf evaporation sites are not enriched – the steady-state assumption would most likely not be adequate.

Non-steady-state Craig-Gordon models allow to describe diurnal dynamics better than steady state models, and would therefore be preferred for ecosystem scale flux partitioning. However, they require independent estimation of the isotopic composition of transpired water (δT), without assuming that this composition is equal to the source water (δxylem), as we have done under the steady-state assumption. In natural ecosystems, δT is not only difficult to measure, it is also complex to estimate independently. Ideally, the isotopic composition of the water at the evaporation site (δe) would be known, so that δT can be solved for reliably. Direct sampling of δe is impossible however, as the actual sites of evaporation are microscopically small. Instead, water samples from complete leaves or leaf lamina might be used to estimate δe by taking into account the Péclet effect. The limit here is that the magnitude of the Péclet effect is highly dependent on hard to determine variables like the effective path length (L, see Eq. ). Estimates for this variable vary considerably between experiments and species . The value L=10 mm that we determined for the 14:00 steady state of the 13 d composite, is in line with previously reported values by for example , who found L=8 mm. While steady-state leaf water assumptions are thus known to be inadequate, the increased complexity of non-steady-state models is hard to take into account in natural ecosystems, posing a limit for applying the ecosystem flux partitioning technique using isotope information to the entire diurnal cycle.

The isotopic steady-state assumption is not applicable to soils due to the comparatively large size of the water reservoir in contact with the atmosphere . This results in diffusion of enriched water from the evaporation sites back into the topsoil water pool. Over time, this results in the gradient we illustrate in Fig. , where the topsoil becomes enriched compared to the deep soil water. This enrichment can be expected to have a limited diurnal cycle, which allows for topsoil water samples to be used to estimate δE for the entire day. The topsoil water enrichment we find during CloudRoots-Amazon22 is very small, with a gradient in δD of 8.6 ‰. instead find gradients in δD reaching 40 ‰ in agricultural fields. The resetting of the gradient by regular precipitation in the Amazon could in part explain this large difference. On top of this, the strong shading from the rainforest canopy, and leaf litter, which limit solar irradiance and thereby E, contributes to the small soil water isotopic gradients in the Amazon.

The work presented in this chapter shows that isotopic flux partitioning is possible and offers insight into the individual gross fluxes. Further implementation of the method is limited by (1) the requirement for local scale sampling measurements to determine the appropriate isotopic end-members, and (2) by the methodological uncertainties and assumptions associated with the method. Still, we consider diurnally resolved individual flux estimates of the net exchange of H₂O and CO₂ to be within reach. Such insights will help to better validate and understand ecosystem behaviour . In addition, describing the diurnal dynamics of the isotopic reservoirs in an ecosystem would enable us to advance understanding of the isotopic budgets of H₂O and CO₂ in the atmosphere by taking into account non-linear land-atmosphere exchange effects .

A logical next step would be to apply isotope-based partitioning on longer (seasonal) time scales – which will require explicit characterization of the seasonal evolution of the relevant isotope reservoirs (soil and leaf water, atmospheric background) – as discussed in for example . In addition, cross-validation of our isotope-based partitioning with other widely used, but debated, NEE partitioning frameworks such as modified daytime and neural-network based methods would be valuable .