On allowing for transient variation in end‐member δ13C values in partitioning soil C fluxes from net ecosystem respiration

The use of stable isotope analysis to resolve ecosystem respiration into its plant and soil components rests on how well the end‐member isotope signatures (δ13C) are characterised. In general, it is assumed that end‐member values are constant over time. However, there are necessarily diurnal and other transient variations in end‐members with environmental conditions. We analyse diurnal and seasonal patterns of ecosystem respiration and its δ13C in a C4 grass growing in a C3 soil using fixed and diurnally varying plant and soil δ13C end‐members. We measure the end‐members independently, and we assess the effects of expected variation in values. We show that variation in end‐members within realistic ranges, particularly diurnal changes in the plant end‐member, can cause partitioning errors of 40% during periods of high plant growth. The effect depends on how close the end‐member is to the measured net respiration δ13C, that is, the proportion of the respiration due to that end‐member. We show light‐driven variation in plant end‐members can cause substantial distortion of partitioned soil organic matter (SOM) flux patterns on a diurnal scale and cause underestimation of daily to annual SOM turnover of approximately 25%. We conclude that, while it is not practicable to independently measure the full temporal variation in end‐member values over a growing season, this error may be adjusted for by using a diurnally varying δ13Cplant.

• Ignoring temporal changes in end-member δ 13 C values can cause large errors in partitioning • Long-term data sets with sufficient temporal resolution can be used to correct for this K E Y W O R D S C 3 and C 4 photosynthesis, ecosystem respiration, isotopic flux partitioning, natural abundance, rhizosphere priming effect, soil carbon

| INTRODUCTION
The effects of plant roots and rhizodeposition on soil organic matter (SOM) turnover remain among the most poorly understood aspects of the terrestrial carbon (C) cycle (Hartmann et al., 2020). A major factor is the difficulty of separating C fluxes from plants and rhizodeposition from those from SOM turnover. One way of doing this is to exploit differences in the C isotope composition of plants and SOM (Brüggemann et al., 2011;Paterson et al., 2009;Werth & Kuzyakov, 2010). Isotopic fractionations occur in most biochemical and biophysical processes, favouring either 12 C or 13 C. Hence, SOM is typically enriched in 13 C compared to the plants from which it was derived by 2‰-4‰ (Bowling et al., 2008). The δ 13 C of the net plant and soil flux will lie between the plant and SOM 'end-member' values (i.e., the values for the plants and soil separately), and so can be used to partition fluxes with a mass balance mixing model. Differences of 2‰-4‰ are close to the quantitation limits of currently available analytical methods. But larger differences can be created, either by labelling plants with CO 2 enriched or depleted in 13 C, or, more practicably under field conditions, by exploiting the large δ 13 C difference between C 3 and C 4 photosynthetic pathways, which is typically 10‰-20‰ (Balesdent et al., 1987;Farquhar et al., 1989). This may be done by growing a C 4 plant in a soil that has previously only hosted C 3 plants, or vice-versa (Rochette & Flanagan, 1997;Wang et al., 2016;Xiao et al., 2015), or with natural δ 13 C gradients across transects of C 3 -C 4 vegetation (Millard et al., 2008). In all cases, however, reliable partitioning of plant and SOM respiration fluxes depends on how well the δ 13 C end-members are characterised. This paper is about how best to do this and how to allow for transient variation in end-members which as yet has been largely overlooked in the flux partitioning literature (Lee et al., 2020;Ogle & Pendall, 2015).
Wide variation in δ 13 C values are reported for C 4 plants and C 3 soils ( Figure 1). The largest variation is between photosynthetic pathways, but there is substantial variation within C 4 plants (À16‰ to À8‰) and C 3 soils (À30‰ to À20‰). Some of this is due to differences in measurement methods, such as with instrument calibration, as well as inherent differences within plant species and soil types. However a large part is due to transient variation driven by environmental factors. Water stress can cause large δ 13 C shifts in C 3 species, but this effect is small in C 4 plants, typically <1‰, owing to their greater water use efficiency (Cernusak et al., 2013;Ghannoum et al., 2002). Of particular importance is climatic, seasonal and diurnal variation in light intensity; this causes differences in both C 3 and C 4 plant δ 13 C of 1‰-8‰ (Cernusak et al., 2013;Cornwell et al., 2018;Ghashghaie & Badeck, 2014). Leaf respiration immediately after a period of illumination is 13 C-enriched, whereas it is progressively 13 C-depleted during darkness. In C 3 grasses, Barbour et al. (2005) observed a decrease in δ 13 C of approximately 5‰ over 6 h of darkness, with the change almost entirely taking place in the first 2 h, and Tcherkez et al. (2003) found a decrease of approximately 10‰ over 5 days in a C 3 forb. There have been fewer studies in C 4 species, but Sun et al. (2010) and Zhong et al. (2017) found decreases from 1‰ to 4‰ (mostly 2‰-4‰) over 6 h of dark in C 4 grasses. The daytime 13 C enrichment is linked to differences in C substrate availability and metabolite partitioning during photosynthesis (Ghashghaie & Badeck, 2014;Sun et al., 2010;Zhong et al., 2017).
Soil isotopic composition is less affected by short-term variation in environmental conditions (Buchman et al., 1997;Scartazza et al., 2004), although environmentally driven variability in microbial fractionation has been observed (Lerch et al., 2011). There is variation in the δ 13 C of SOM pools and respiration with soil depth, in part due to differences between litter and SOM ( Figure 1) but also due to biophysical processes (Boström et al., 2007;Nickerson & Risk, 2009;Trudell et al., 2004). Inputs of plant residues and root exudates vary with depth and follow seasonal patterns, and differences in the rates of decomposition of different inputs add to temporal variation in the δ 13 C of cycling SOM pools (Werth & Kuzyakov, 2010). Hence, the δ 13 C of SOM respiration may differ from that of the bulk SOM and may also vary over a season. Few studies have measured the δ 13 C of both bulk root-free soil and its respiration, and those that have report contrasting differences (Boström et al., 2007;Pausch & Kuzyakov, 2012). Fractionation between microbial biomass (itself more 13 C enriched than SOM) and microbial respiration is highly variable, ranging from +4.3‰ to À3.2‰ (Werth & Kuzyakov, 2010). Further, in a C 3 to C 4 vegetation change, the C 4 inputs will gradually become incorporated into the SOM, potentially providing a means of separating SOM pools but also complicating end-member evaluations.
What does this mean for partitioning soil C fluxes and whether or not to allow for transient variation in end-member δ 13 C values? Although temporal variation in end-members has been allowed for in partitioning photosynthetic and respiration fluxes in net CO 2 exchange (Fassbinder et al., 2012;Wehr & Saleska, 2015), as far as we are aware, the effects have not been assessed for partitioning plant and soil respiration fluxes. In principle, partitioning errors on diurnal and other short timescales can affect both the inferred short-term variation in SOM fluxes and longer-term seasonal and annual dynamics and resulting conclusions about plant and soil processes. In this paper, we explore this with a data set of diurnal and seasonal patterns of C fluxes and δ 13 C in a C 4 plant-C 3 soil field system. We focus on diurnal variation in the plant end-member given its inevitability and known importance. We use as baseline end-members the δ 13 C of plant and soil dry matter sampled from the field, which integrate short-term variations (Cernusak et al., 15 Rochette and Flanagan (1997);Wedinet al. (1995); Werth and Kuzyakov (2006); Zhu and Cheng (2011) shoot tissue 102 Ghannoum et al. (2002); Hattersley (1982); Weiguo et al. (2005); Rochette and Flanagan (1997); Sun et al. (2010);von Caemmerer et al. (2014); G. Wang et al. (2005); Wedin et al. (1995); Werth and Kuzyakov (2006 (b) Numbers of reported values (n; NB in studies with treatment replicates n = 1) and references. Studies were excluded where plants were not grown under atmospheric δ 13 C conditions, for soil organic matter (SOM) respiration where roots were not excluded, and where only relative fractionation of 13 C (rather than δ 13 C) was given 2013). We assess the sensitivity of partitioning to the plant and soil end-members within realistic ranges, and the effect of diurnal changes in the plant end-member.

| Respiration measurements and partitioning
Measurements were made using the field laboratory system described in McCloskey et al. (2020). Briefly, the system contains 24 0.8-m diameter, 1-m deep soil monoliths in lysimeters, connected to automated gas-flux chambers and instruments for gas and stable isotope measurements. The data used in this analysis are for 12 lysimeters of a poorly drained, seasonally waterlogged loamy soil over clay, formerly under old C 3 pasture at Temple Balsall, Warwickshire and sampled as undisturbed, naturally structured monoliths. The soil was sown with C 4 buffalo grass (Bouteloua dactyloides) in January 2018 and then maintained under ambient field conditions, with periodic clipping to maintain an approximately 10-cm high sward. During a plant and soil respiration measurement, an opaque lysimeter chamber is closed with an opaque lid and air in the headspace is circulated via a sampling loop to a gas analyser (Picarro G2201-i cavity ring-down spectroscopy instrument, calibrated against a Thermo Finnigan Delta Plus XP isotope ratio mass spectrometer as described in McCloskey et al., 2020) for near continuous measurement of the headspace CO 2 concentration and its δ 13 C. The total sampling and measurement interval is approximately 20 min, allowing three measurements in each of the 12 lysimeters over 24 h. The combined plant and soil respiration flux (F R ) is found from the rate of change in headspace concentration after a period of equilibration, and its isotope ratio (δ 13 C R ) is found from plots of δ 13 C versus the inverse of the CO 2 concentration according to the Keeling plot method (McCloskey et al., 2020). The flux is then partitioned between C 3 SOM and C 4 plant sources as follows. By definition and where δ 13 C ¼ 13 C= 12 C ð Þ sample = 13 C= 12 C ð Þ standard À 1 h i Â1000, δ 13 C plant and δ 13 C SOM are the plant and SOM endmember values, and f plant and f SOM are the proportion of the total flux attributable to plant or SOM sources, respectively. Combining Equations (1)-(4) and rearranging gives and 2.2 | End-member measurements

| From plant and soil dry matter
For the δ 13 C of plant material, grass shoot clippings were taken on 3-4 October 2019 from six randomly selected lysimeters. The samples were dried at 65 C to constant weight and ground in a planetary ball-mill (Fritsch Pulverisette 6, Gerhardt, Brackley, UK) for 6 min at 300 rpm. The samples were analysed for δ 13 C by combustion using a Delta Plus XP IRMS connected via a Conflo III to a Flash EA 1112 Series Elemental Analyser (all Thermo Finnigan, Bremen, Germany). Six replicate sub-samples from each sampled lysimeter were analysed.
For δ 13 C of soil material, bulk soil was sampled in April 2018 (before seeding with B. dactyloides) by taking 2-cm diameter cores to 10-cm depth with a stainless steel auger. Ten samples were taken from each of four randomly selected lysimeters, air dried and bulked for each lysimeter. Sub-samples of the soil were ground using a pestle and mortar to pass a 2 mm sieve and analysed by combustion as for the plant material.

| From respiration
For the δ 13 C of soil flux, air-dry samples of the original field soil, unexposed to the C 4 grass, were moistened to field capacity, packed to a depth of 3 cm in 15-cm internal diameter plastic pipes with acrylic disks glued to their bases, and incubated for 41 days at ambient laboratory temperature. A pneumatically-operated gas flux chamber (eosAC, Eosense, Nova Scotia, Canada) was fitted on top, and connected to a Picarro G2201-i analyser via a multiplexer (eosMX, Eosense) and Picarro A0702 diaphragm pump. Measurements of CO 2 respired and its δ 13 C were taken over 22 min and δ 13 C SOM obtained using Keeling plots. Two replicate mesocosms were used, with seven repeated measurements per mesocosm.
For the δ 13 C of plant flux, seeds of B. dactyloides were germinated and sown in moist sand that had been heat treated to remove organic matter and packed into plastic pipes as for the δ 13 C SOM measurements. The grass was then grown for 2 months in a glasshouse under ambient summer lighting with watering to constant weight. Respiration measurements were made by bringing the mesocosms into an indoor laboratory and attaching flux chambers over the grass in the dark as for the δ 13 C SOM measurements, with a 17 min measurement period, and δ 13 C plant was obtained using Keeling plots. Three replicate mesocosms were used, with four repeated measurements per mesocosm.

| Sensitivity analysis
To assess the effect of variation or uncertainty in endmember values, we conducted a sensitivity analysis using flux data gathered as above over periods when the grass was actively growing (2-7 August 2018). We partitioned the measured fluxes using end-member values spanning the ranges presented in Figure 1: δ 13 C SOM = À21‰, À24‰, À27‰ and À30‰ with δ 13 C plant = À14.2‰ (as measured on dry plant material); and δ 13 C plant = À10‰, À12‰, À14‰, and À16‰ with δ 13 C SOM = À28.8‰ (as measured on dry soil material). We calculated daily means, maxima and minima of F SOM and F plant over the measurement periods for all δ 13 C SOM and δ 13 C plant values. Data analysis was conducted using R version 3.5.1 (R Core Team, 2017).
To assess the effect of a diurnal shift in δ 13 C plant in partitioning flux data, we compared a fixed δ 13 C plant = À14.2‰ (as measured on dry plant material) with a value enriched under light conditions by 3‰ (based on the 2‰-4‰ variation discussed in Introduction), both with fixed δ 13 C SOM = À28.8‰ (as measured on dry soil material). For simplicity, the plant end-member was treated as either the dark or light value, without a gradual transition. We also tested the effect of more gradual diurnal variation with simulated sinusoidal changes in F R , δ 13 C R and δ 13 C plant with peaks at midday. We reason that the δ 13 C plant of night-time respiration will more-closely track the long-term average value, indicated by the dry plant matter value, and the day-time value will represent the perturbation caused by altered substrate availability and metabolite partitioning during photosynthesis. Day-time conditions were defined as when incoming solar radiation ≥0.05 W m À2 nm À1 , as measured by a weather station (Vaisala WXT520) on the site. In principle, it would be possible to systematically fit a variable end-member value to the data set using model-data fusion techniques. We have not done so because the objective of this study is to illustrate the importance of allowing for timevarying end-members, rather than a broader exploration of model-data fusion methods.
Total daily SOM respiration for each day over the growing season was found by fitting a natural cubic spline to the measured data and calculating the area under the resulting curve. Days for which >6 measurements (out of the target 36) were missed (because of photosynthesis measurements, system maintenance or other reasons) were excluded. Cumulative SOM respiration over the season was then found by fitting a cubic spline to the daily SOM respiration data obtained.

| RESULTS
3.1 | Measured respiration and δ 13 C R Diurnal patterns in both total flux magnitude and δ 13 C were found for plant and soil respiration (Figure 2). In July (when the grass sward was still becoming established) and August (when grass growth was most active), diurnal patterns in both the total flux magnitude and its δ 13 C are clear, with δ 13 C values higher in August than July. In December (when the grass was dormant), the fluxes are smaller, and there are no clear diurnal patterns to either the total flux or its δ 13 C. In July and August, the respiration flux peaks after midday, matching diurnal variation in solar radiation and air temperature ( Figure 3). The δ 13 C of respiration also peaks after midday with a maximum value 2‰-4‰ less negative than the night-time minimum.

| End-member values
The δ 13 C plant values measured from night-time respiration were <1‰ more negative than those from plant dry matter (Table 1). The C 3 soil material had δ 13 C approximately 16‰ more negative (i.e., more 13 C depleted) than the plant material. The δ 13 C SOM values measured from respiration fluxes were approximately 2‰ more negative than those from bulk soil material. These differences in δ 13 C plant and δ 13 C SOM between dry matter and respiration methods are within ranges expected for transient processes driven by environmental variability, as well as artificial biases between the methods. Based on the dry mater values averaging over transient variations, we take these as the standard values for the sensitivity analysis.

| Sensitivity analysis
The sensitivities of partitioned plant and soil fluxes to δ 13 C plant and δ 13 C SOM in early August (when grass growth was greatest) are shown in Figure 4. The daily mean, minimum and maximum fluxes averaged over the measurement period are shown, with δ 13 C plant and δ 13 C SOM values varied over the ranges indicated in Figure 1. In this period, the apparent F plant values are up to an order of magnitude greater than F SOM , depending on the end-member values. The difference decreases as growth declines and in December mean F SOM is greater than mean F plant at most end-member values tested (Supporting information Figure S1).
The effects of end-member values depend on how far they differ from δ 13 C R . Since in most cases δ 13 C SOM < δ 13 C R < δ 13 C plant , it follows from Equation (5) that increasing δ 13 C SOM with δ 13 C plant constant, and increasing δ 13 C plant with δ 13 C SOM constant, both result in an increase in f SOM , that is a greater proportion of the flux comes from the soil. However, where δ 13 C SOM is more enriched than δ 13 C R the calculated F plant is negative, and vice versa. Negative night-time respiration fluxes are impossible, so this can be used to constrain the possible bounds of δ 13 C SOM and δ 13 C plant . From Figure 4 this limits δ 13 C SOM in our system to values more depleted than approximately À25‰ and δ 13 C plant to values more enriched than approximately À15.5‰.
Diurnal trends in simulated SOM fluxes were found to be substantially affected by a diurnal shift in the plant δ 13 C end-member on simulated SOM fluxes ( Figure 5). For simplicity, the diurnal changes in F R , δ 13 C R and δ 13 C plant are sinusoidal with midday peaks and midnight troughs, and the maximum and minimum F R and δ 13 C R values are set to be similar to those for August in Figure  2. It will be seen that with no day-night shift in δ 13 C plant , the SOM flux reaches a minimum at midday as δ 13 C R peaks, in spite of the peak in F R . This would require some F I G U R E 2 Total plant and soil CO 2 fluxes and their δ 13 C signatures from (a) 5-9 July, (b) 2-7 August and (c) 22-27 December 2018. Data are measurements from 12 lysimeters, each measured thrice daily; individual points represent a measurement from a single lysimeter. Solid lines indicate midnight; dashed lines indicate midday negative priming effect, offsetting the expected daytime increase in F SOM with temperature, so is not realistic. However, Figure 5 shows that with a day-time increase in δ 13 C plant of at least +1‰, which is consistent with literature values (Introduction), there is a more-realistic day-time peak in F SOM . The impact of a diurnally varying δ 13 C plant is substantial, with a 3‰ shift resulting in a 44% higher daily SOM flux. The SOM fluxes for 0‰, +1‰, +3‰ and +5‰ shifts in Figure 5 are 3.79, 4.41, 5.47 and 6.36 μmol m À2 d À1 , respectively. This suggests an upper bound to the underestimation of diel SOM of approximately 40%. Clear diurnal patterns in both plant and SOM fluxes are evident in July using fixed δ 13 C plant and δ 13 C SOM values equal to the dry matter values (À14.2‰ and À28.8‰, respectively), with both fluxes peaking after midday (Figure 7). However in August, when plant F I G U R E 3 Diurnal changes in solar radiation and temperature from (a) 5-9 July and (b) 2-7 August 2018. Temperature data are measurements from 12 lysimeters measured thrice daily; individual points represent a measurement from a single lysimeter. Solid lines indicate midnight; dashed lines indicate midday growth and respiration are greater, there is little diurnal variation in SOM fluxes, with small peaks around midnight, though the plant fluxes show the same diurnal pattern as in July and peak after midday. In December, both fluxes are small without clear diurnal trends.
Comparing fluxes partitioned using a fixed plant endmember (Figure 6a-c) with those using a diurnal change in δ 13 C plant of 3‰ (Figure 6d-f), it is clear that the former results in an underestimation of the SOM flux, and an overestimation of the plant flux. These differences are largest when the system is dominated by plant respiration. Once the diurnal enrichment of δ 13 C plant is accounted for, plant and SOM fluxes in August show show sensitivity to δ 13 C SOM at the δ 13 C plant measured on plant material; right-hand panels (c, d) show sensitivity to δ 13 C plant at the δ 13 C SOM measured on soil material. The mean total flux δ 13 C over this period was À17.3 ± 0.1‰. Data are means ± SE F I G U R E 5 Simulated sensitivity of soil organic matter (SOM) C flux (F SOM ) to a night-day shift in the plant end-member (δ 13 C plant ; numbers on curves). The diurnal variation in total C flux (F R ), its isotope signature (δ 13 C R ) and δ 13 C plant are simulated as sinusoidal with peaks at midday. The soil end-member is constant, and F SOM is calculated with Equations (3) and (5) similar patterns to those in July, with peaks in both fluxes after midday. Increased f SOM with the less negative day-time δ 13 C plant is expected from Equation (5). We also found, with fixed δ 13 C SOM = À28.8‰ and δ 13 C plant = À11.2‰, the diurnal plant and SOM respiration patterns in July and August were aligned, both peaking after midday (Supporting information Figure S2). The main changes compared to Figure 6 are that in July, the nighttime SOM and plant fluxes are roughly equal; in August, the diurnal variation in the SOM flux is reduced; and in December, the SOM flux is generally greater than the plant flux, rather than roughly equal. Allowing for a diurnal shift in δ 13 C plant on the cumulative SOM respiration over the 2018 growing season has a substantial effect, increasing total SOM respiration by 26% from July to December (Figure 7). The majority of this difference occurred between mid-July and mid-September, when plant respiration was most dominant.

| Effects of varying end-members
Our results show that allowing for a diurnally varying plant end-member produces large differences in apparent F I G U R E 7 Effect of allowing for a +3‰ diurnal shift in the plant δ 13 end-member on cumulative soil organic matter (SOM) respiration over the 2018 growing season F I G U R E 6 Partitioned plant and soil organic matter (SOM) C fluxes with δ 13 C SOM = À28.8‰ and (a-c) δ 13 C plant = À14.2‰ or (d-f) a +3‰ daytime shift in δ 13 C plant (À14.2‰ at night, À11.2‰ during the day) from 5-9 July, 2-7 August and 22-27 December 2018, respectively. Data are measurements from 12 lysimeters, and each measured thrice daily; individual points represent a measurement from a single lysimeter. Solid lines indicate midnight; dashed lines indicate midday SOM turnover on diurnal and seasonal time scales, and an apparent tight coupling with photosynthesis. Although changes in end-members are to be expected with variations in light intensity, temperature, moisture and other variables (Introduction), we believe this is the first study to quantify the consequences for partitioning of plant and soil C fluxes under field conditions. We have focused on the plant end-member because there are necessarily large diurnal changes in it-of the order of 1‰-5‰-driven by changes in light intensity in both C 3 and C 4 plants ( Barbour et al., 2005;Sun et al., 2010;Tcherkez et al., 2003;Zhong et al., 2017). In our system, not accounting for this diurnal variation resulted in underestimation of SOM turnover by 26% over 6 months, or up to 40% per day during the height of the growing season. The effect of diurnal δ 13 C plant changes varies with plant growth over the season. In early July, when the grass sward was still becoming established, clear diurnal patterns in total C flux, its δ 13 C and the SOM flux obtained with or without a varying plant end-member were apparent, along with strong diurnal variation in solar radiation and temperature. During this period, the SOM flux obtained with fixed end-member values measured on plant and soil dry matter was comparable to the plant flux, and a diurnal pattern in SOM fluxes was evident with a peak after midday. This is the expected pattern due to the well-established effects of diurnal changes in temperature on plant and soil respiration (Phillips et al., 2011;Vargas et al., 2011). However in August, when the grass sward was better established and plant respiration a much larger proportion of the total C flux, there was little apparent diurnal variation in SOM turnover if the end-members were constant. From the expected effect of diurnally varying temperature, and our July results, these apparent August SOM fluxes are evidently erroneous. We obtained a more realistic diurnal pattern when we allowed for a diurnally-varying plant end-member.
The grass sward was not fully established in July, but it was well established in August, and the plant flux was a substantially larger proportion of the net flux. The distortions of partitioned SOM fluxes in August but not July were thus due to the greater dominance of plant respiration. The daytime increase in the measured 13 C enrichment of the total flux results in an exaggerated partitioning in favour of the plant flux. With increasing dominance by the plant flux, this distorts flux partitioning to the point that daytime SOM flux peaks disappears or even becomes inverted, as we saw in the sensitivity analyses. As a 13 C enrichment of both C 3 and C 4 respiration during photosynthesis is expected (Introduction), we consider not allowing for it to be the likely cause of the inverted SOM flux peaks we observed in August.

| Alternative explanations for diurnal patterns
An alternative explanation is that the real plant endmember, while stable over diurnal timescales, was more 13 C enriched than the value we used. We also reproduced the daytime SOM respiration peak with a fixed plant endmember more 13 C-enriched than the measured dry matter value by 3‰. However, we see no reason why the measurement of δ 13 C plant in dry matter should misrepresent the long-term average δ 13 C plant to this extent, given that the plant flux measured under dark conditions was less enriched than the dry matter measurement.
No daytime increase in SOM flux, in spite of the daytime soil warming, might be expected if soil microbes preferentially used root exudates rather than SOM as their carbon source, as root exudation increases during the day (Bahn et al., 2009). Against this, SOM turnover may be enhanced by priming effects of root exudates, whereby exudates provide energy for microbes to 'mine' limiting nutrients from SOM (Paterson et al., 2009;Werth & Kuzyakov, 2010). Therefore, a daytime increase in SOM flux is expected both due to the effects of daytime warming and priming effects. The fact that the postmidday peaks in SOM flux ( Figure 6) closely match the peaks in solar radiation (Figure 3), and more closely than the peaks in soil temperature which occur earlier in the day (Figure 3), suggests a tight coupling between solar radiation and the SOM flux. To the extent that root exudation varies closely with solar radiation (Bahn et al., 2009;Kuzyakov & Gavrichkova, 2010), this is good evidence for priming effects. We conclude that a diurnally varying SOM-flux linked to a diurnally varying plant end-member is more consistent with theoretical expectations than a diurnally constant SOM flux.
In our system, both above-and below-ground respiration are measured, and so plant respiration is the predominant component during the main growing season. Errors in δ 13 C plant have a correspondingly large effect on the calculated SOM flux. This effect will be less in systems that exclude above-ground respiration. However, it is nonetheless necessary to allow for diurnal shifts in the plant endmember as root respiration and exudation vary diurnally with photosynthesis (Bahn et al., 2009;Kuzyakov & Gavrichkova, 2010).

| Implications for measuring SOM turnover
How should temporal changes in end-members be quantified and allowed for? Baseline end-members can be characterised either by directly sampling respiration fluxes or by measuring the δ 13 C of plant and soil dry matter. The δ 13 C of dry matter, produced during varying environmental conditions, provides a long-term integration of temporal variation (Cernusak et al., 2013). This applies to both the plant end-member, which is particularly subject to variation with light intensity as we have seen, and the soil end-member, which is particularly subject to variation with recent C inputs, which make up only a small fraction of the total soil C. A more systematic approach is to use model-data fusion methods to fit variable end-members to a data set gathered across a growing season, parsimoniously selecting parameters consistent with the full data set (Ogle & Pendall, 2015;Phillips et al., 2017). Prior values of end-members for this can be set using the δ 13 C of plant and soil dry-matter samples.
We have shown that allowing for short-term variation in flux partitioning is important for correctly quantifying daily and seasonal patterns in SOM fluxes. Information at such time-scales is needed to explore biotic and abiotic processes controlling SOM dynamics, particularly rootsoil-microbe interactions and priming effects. Until recently, such processes have not been well represented in SOM models, but the need to do so is widely discussed (Wieder et al., 2015). Inclusion of priming effects in SOM models results in qualitatively different medium and long-term predictions, including at global scales (Guenet et al., 2018;Woof & Lehmann, 2019;Wutzler et al., 2017). However, progress in defining minimal models for these purposes is constrained by the availability of reliable data on priming and other effects under field conditions. The points discussed here need to be allowed for in using isotope fractionation methods to obtain such data.

| CONCLUSIONS
1. There is necessarily transient variation in plant and soil δ 13 C end-members over the course of a growing season and on diurnal timescales, due to varying environmental conditions. Large diurnal variation in the plant end-member is well established, but is generally not accounted for when using δ 13 C to partition soil and plant fluxes. 2. In our experiments, not allowing for diurnal variation in the plant end-member caused partitioning errors of 26% over a season and 40% over a day during periods of high plant growth. 3. Potential errors are greatest when the end-member is far from δ 13 C of the total flux, or the total flux is small, so that a small change in flux has a proportionally greater effect.