2.1 Soil sampling and incubation preparation

For the EUR campaign, the superficial 10 cm of soil was sampled at three locations within each of the 27 sites during the Northern Hemisphere summer of 2016 (Fig. S1a in the Supplement). These sites represented a range of forests (n=16) and grasslands (n=6) located in subarctic (Dfc; n=6), temperate oceanic (Cfb; n=13), hot-summer Mediterranean (Csa; n=7) and hot semi-arid (Bsh; n=1) climate zones. In addition, we also sampled an agricultural field (n=1), a peatland (n=1) and some orchards (n=3). Soil samples were transported at ambient temperatures to the Bordeaux-Nouvelle Aquitaine Center of the National Institute of Agricultural and Environmental Research (INRAE), France. Upon arrival, samples were passed through a 4 mm sieve and mixed to create one homogeneous sample for each site. These soils were stored at 4 ^∘C. A sub-sample of each of these soils was used to determine the initial water content and the soil water-holding capacity (Haney and Haney, 2010). For each soil three replicated incubations were prepared with glass jars of 15.54 cm in height and an internal diameter of 8.74 cm. Each jar was filled with the wet weight equivalent of 115 to 300 g of dry soil and the water content adjusted to 30 % of the water-holding capacity to create a soil column with a surface area of 60.0 cm² and a depth of approximately 4 to 7 cm. The jars were then pre-incubated in a climate-controlled cabinet (MD1400, Snijders, Tilburg, NL) for 2 weeks in the dark at 22±1 ^∘C. This cabinet was continuously flushed with approximately 20 L min⁻¹ of ambient air provided by a pump with an intake line outside the building to avoid exposing the soil to elevated CO₂ concentrations found within the laboratory. During this period, soil water content was periodically adjusted to account for evaporation. Approximately 18 h prior to measurement the jar was closed with a screw-tight glass lid equipped with inlet and outlet connections and flushed at 250 mL min⁻¹ with dry, synthetic air to promote steady-state conditions. This flow was produced using an in-house dilution system that mixed pure CO₂ from a cylinder into CO₂-free air generated by an air compressor (FM2 Atlas Copto, Nacka, Sweden) equipped with a scrubbing column (Ecodry K-MT6, Parker Hannifin, USA). This system was set to achieve a CO₂ concentration of 400±5 ppm and, reflecting the origin of the CO₂ in the cylinder used, had a δ¹⁸O of approximately −25 ‰ VPDB_g. Subsequently the jar was removed to conduct gas exchange and soil property measurements.

For the AUS campaign, we sampled the superficial 10 cm of soil at four locations within each of the 17 sites during July of 2017 and returned these samples on the same day to the Cairns campus of James Cook University (Fig. S1b). These sites fell within tropical monsoon (Am; n=3), humid subtropical (Cfa; n=9) and monsoon-influenced humid subtropical (Cwa; n=5) climate zones and were principally found in forests (n=9) and savannas (n=6), with the other remaining sites located in a pasture (n=1) and a stunted shrub-rich forest (n=1). These soils were passed through a 4 mm sieve and mixed to create a homogenous sample for each site. A sub-sample of each of these soils was used to determine the initial water content and estimate the re-packed bulk density of the soils. As with the EUR campaign, three replicate incubations were prepared in glass jars for each soil. These jars had a height of 11.56 cm and an internal diameter of 7.45 cm. A jar was filled with the wet weight equivalent of 215 to 450 g of dry soil and the water content adjusted to 30 % water-filled pore space to create a soil column with a surface area of 43.5 cm² and a depth of approximately 8.5 cm. The jar was then pre-incubated in an insulated box for 1 week in the dark at 23±1 ^∘C with periodic adjustments to the water content to account for evaporation. This box was continuously flushed with approximately 10 L min⁻¹ of air provided by a compressor that serviced building-wide laboratory air distribution. The concentration of CO₂ in this air was approximately 420 ppm and, reflecting its atmospheric origin, had a δ¹⁸O of approximately 0 ‰ VPDB_g. Following pre-incubation the jar was removed to conduct gas exchange and soil property measurements.

An NH₄NO₃ addition experiment was also conducted in both campaigns. This involved the preparation of three additional replicated incubations as described above, for nine of the EUR sites and five of the AUS sites. Prior to the pre-incubation step, 0.7 mg of NH₄NO₃ g dry soil⁻¹ was dissolved in water and used to adjust the water content of these additional replicate incubations. These were then incubated alongside the three other “control” incubations prepared as part of the spatial survey described above. The quantity of NH₄NO₃ applied was chosen to approximate a fertilisation treatment comparable to those typically applied in field studies (Ramirez et al., 2012).

2.2 Gas exchange measurements

Gas exchange measurements were made using a similar experimental set-up to that described in Jones et al. (2017). Each jar was connected to a gas delivery system that supplied one of two gas sources, δ_b,atm or δ_b,mix, to its inlet. The first inlet condition, δ_b,atm, consisted of a continuous flow of atmospheric air pumped from an external buffer volume, through a Drierite column (W. A. Hammond Drierite Co. Ltd, USA) to dry the air and directly to the inlet of the jar. The second condition, δ_b,mix, was produced by a second continuous flow of atmospheric air pumped from the buffer, through a soda lime column to remove CO₂ and a second Drierite column. A mass-flow controller was used to dilute pure CO₂ from a cylinder into this dry CO₂ free air, and then this mix was supplied to the inlet of the jar. The flow rate of pure CO₂ was controlled to match the concentration of the CO₂ in δ_b,mix to that of δ_b,atm using a control loop feedback based on the difference in concentration between sub-samples of both flows measured with an infrared CO₂ analyser (Li-6262, LI-COR Biosciences, USA). By doing so the principal difference between the two conditions was the isotopic composition of the CO₂ present reflecting its origin in the atmosphere (δ¹⁸O–CO₂ of ${\mathit{\delta }}_{\text{b,atm}}=-\mathrm{1.41}\pm \mathrm{2.17}$ ‰ VPDB_g) or a cylinder (δ¹⁸O–CO₂ of ${\mathit{\delta }}_{\text{b,mix}}=-\mathrm{25.33}\pm \mathrm{0.30}$ ‰ VPDB_g). Following this system the selected gas flow was split into a chamber line with a flow rate of 171.48 µmol s⁻¹, to which the jar was connected, and a bypass line that was measured by a CO₂ isotope ratio infrared spectrometer (Delta Ray IRIS, Thermo Fischer Scientific, Germany). The gas supply system sequentially supplied the two inlet conditions to these measurement lines. Both inlet conditions were supplied for either 32 (EUR) or 34 (AUS) minutes. The first 20 (EUR) or 22 (AUS) minutes under each condition were used to flush the system and promote steady-state conditions in the incubation jar. The turnover time of air in the jar was less than 10 min. After this period, the final 12 min during which the condition was supplied was used for gas-exchange measurements. During this period the IRIS measured the chamber and bypass lines three times each for 2 min. Calibration gas was measured every 16 (EUR) or 18 (AUS) minutes with sequential 2 min measurements of two cylinders containing synthetic air with different CO₂ concentrations but similar isotopic compositions. The concentrations of ¹²C¹⁶O¹⁶O, ¹³C¹⁶O¹⁶O and ¹²C¹⁸O¹⁶O recorded by the IRIS were processed as described in detail by Jones et al. (2017) to average the final 40 s of data collected for each measurement and calculate corrected concentrations and isotope ratios. The associated precision for the total concentration and δ¹⁸O of CO₂ was 0.02 ppm and 0.06 ‰ VPDBg, respectively.

Reflecting the pre-incubation conditions, measurements for EUR began with δ_b,mix as the inlet condition before switching to δ_b,atm, whilst for AUS the sequence began with δ_b,atm and then switched to δ_b,mix. For EUR, the calibration cylinders (21 % O₂ and 0.93 % Ar in a N₂ balance, Deuste Steininger GmbH, Germany) had a total concentration, carbon isotope composition and δ¹⁸O of CO₂, respectively, of 380.26 ppm, −3.06 ‰ VPDB and −14.63 ‰ VPDB_g for the first cylinder and 481.62 ppm, −3.07 ‰ VPDB and 14.70 ‰ VPDB_g for the second cylinder (IsoLab, Max Planck Institute for Biogeochemistry, Germany). For AUS, the calibration cylinders (21 % O₂ and 1.12 % Ar in a N₂ balance, BOC, Australia) had a total concentration, carbon isotope composition and δ¹⁸O of CO₂, respectively, of 386.7 ppm, −33.42 ‰ VPDB and −26.33 ‰ VPDB_g for the first cylinder and 486.7 ppm, −33.64 ‰ VPDB and −26.60 ‰ VPDB_g for the second cylinder (Farquhar Laboratory, Australian National University, Australia).

The net CO₂ flux, F_R ($\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$), was calculated from corrected values for the three pairs of chamber and bypass line measurements made at each inlet condition following Eq. (1):

where u is the flow rate (mol s⁻¹) through the chamber line, C_c is the total CO₂ concentration (ppm) of the chamber line, C_b is the total CO₂ concentration (ppm) of the bypass line and A is the surface area (m²) of the soil in the chamber. The resultant three values for each inlet condition were then averaged to yield a single flux rate. Similarly, the δ¹⁸O of CO₂ exchange, δ_R (‰ VPDB_g), was calculated following Eq. (2):

where δ_c is the δ¹⁸O of CO₂ (‰ VPDB_g) in the chamber line, δ_b is the δ¹⁸O of CO₂ (‰ VPDB_g) in the bypass line, C_c,12 (ppm) is the concentration of ¹²C¹⁶O¹⁶O in the chamber line and C_b,12 (ppm) is the concentration of ¹²C¹⁶O¹⁶O in the bypass line.

2.3 Soil properties

After being disconnected from the gas exchange system, a jar was weighed to determine the wet weight of the incubated soil and the total soil depth, z_max (m), measured using a caliper. Soil was then removed from the jar to determine soil water content, pH, microbial biomass, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$. Soil water contents were determined gravimetrically for sub-samples based on water loss after oven drying for 24 h at 105 ^∘C. In the EUR campaign, soil water content was determined for three 1.5 cm thick intervals between 0 and 4.5 cm depth. An average gravimetric water content (g g dry soil⁻¹) was calculated for the soil column after weighting by total soil depth. In the AUS campaign, soil water content was determined for a single sample covering the total soil depth. Soil bulk density (g cm⁻³) was calculated from the gravimetric water content, the wet weight of the soil in the jar and the volume of the soil column. Total porosity, ϕ_t, was calculated from bulk density assuming a particle density of 2.65 g cm⁻³ (Linn and Doran, 1984). Volumetric water content, θ_w (m³ m⁻³), was calculated as the product of gravimetric water content and bulk density. The soil air-filled porosity, ϕ_a, was calculated as the difference between the total porosity and volumetric water content. The remaining soil column in the jar was then mixed and sub-samples were taken to determine pH, microbial biomass, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$. Soil pH was determined in a slurry with a dry weight equivalent soil-to-water ratio of 1:5. Soil microbial biomass (µg C g dry soil⁻¹) was determined based on the difference between dissolved carbon extracted from non-fumigated and chloroform-fumigated sub-samples using a slurry with a dry weight equivalent soil-to-potassium sulfate solution (0.5 M) ratio of 1:5 and an extraction efficiency value of 0.35. Exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (µg N g dry soil⁻¹) and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (µg N g dry soil⁻¹) were extracted in a slurry with a dry weight equivalent soil-to-potassium chloride solution (1 M) ratio of $\mathrm{1}:\mathrm{5}.$ These extracts were filtered, frozen at −20 ^∘C and shipped on dry ice to commercial laboratories (EUR: LAS INRAE Hauts-de-France, Arras, France; AUS: ASL Environmental, Brisbane, Queensland, Australia) for determination of dissolved carbon, ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ concentrations. Sub-samples of the homogenised soil used to fill jars in the EUR campaign were also taken to determine soil texture and carbon and nitrogen content by sampling site as part of a related study (Kaisermann et al., 2018a).

2.4 Estimating the oxygen isotope exchange rate

Following Jones et al. (2017), the rate of oxygen isotope exchange between soil water and CO₂, k_iso, was estimated from the inverse of the slope of the linear relationship between the δ¹⁸O of CO₂ exchange and the δ¹⁸O of CO₂ at the soil surface. Briefly, under the two gas-exchange measurement conditions induced by varying the δ¹⁸O of CO₂ at the incubation inlet (δ_b,mix and δ_b,atm), the invasion flux or piston velocity of CO₂, v_inv (m s⁻¹), can be estimated following Eq. (3):

where δ_R (‰ VPDB_g) is the δ¹⁸O of CO₂ exchange and δ_a (‰ VPDB_g) is the δ¹⁸O of CO₂ at the soil surface under the two different inlet conditions (δ_b,mix and δ_b,atm) and F_R,μ ($\mathrm{\mu }\mathrm{mol}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{s}}^{-\mathrm{1}}$) is the mean net CO₂ flux under both conditions and C_a,μ (µmol m⁻³) is the mean total CO₂ concentration at the soil surface measured under both conditions. Both δ_a and C_a were assumed equal to the δ_c and C_c measured in the chamber line as discussed previously. To correct for the influence of boundary conditions found at the bottom of incubation jars, particularly in shallower soil columns, the soil-depth-adjusted invasion flux, ${\stackrel{\mathrm{̃}}{v}}_{\text{inv}}$ (m s⁻¹), was determined iteratively to satisfy Eq. (4):

where z_max (m) is the total soil-column depth, κ is soil tortuosity calculated here following the formulation of Moldrup et al. (2003) for repacked soils, D (m² s⁻¹) is the diffusivity of ¹²C¹⁶O¹⁸O in air (Massman, 1998; Tans, 1998) and ϕ_a is the air-filled porosity of the soil (see Sauze et al., 2018, for the derivation). Subsequently k_iso (s⁻¹) was calculated following Eq. (5):

where B (m³ m⁻³) is the Bunsen solubility coefficient for CO₂ in water (Weiss, 1974) and θ_w (m³ m⁻³) is the soil volumetric water content.

2.5 Statistical analyses

Statistical analyses were conducted in R version 3.5 (R Core Team, 2019). Of the 174 individual incubations prepared, 10 were excluded from the dataset because a record for one of the variables of interest, the rate, k_iso, of oxygen isotope exchange, pH, microbial biomass, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ or exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$, was missing. For the remaining 164 incubations with complete records, these variables were averaged by sampling site and, for the relevant subset, by whether they received a NH₄NO₃ addition.

The resultant dataset consisted of mean observations for 44 untreated soils (n=27/EUR and 17/AUS) and 14 soils (n=9/EUR and 5/AUS) that received a NH₄NO₃ addition. Spatial controls on k_iso were investigated across the means of untreated soils. Correlations between k_iso, pH, microbial biomass, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ were investigated through Spearman's rank correlation between pairs of variables. To test the outlined hypotheses, a multiple generalised linear modelling approach was used to investigate which variables best explained variations in k_iso (Thomas et al., 2017). As pH and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ were strongly negatively correlated (Spearman's $\mathit{\rho }=-\mathrm{0.73}$), they were not considered together in the same model, whilst all other possible combinations, including the sampling campaign (EUR or AUS) to test for the undue influence of systematic experimental differences, were tested. Combinations were limited to models containing four or less predictive terms to prevent over-fitting, and each independent variable was centered and scaled to facilitate comparison among the different measurement scales. The model structure and predictive terms included in the minimal adequate model required to explain variations in k_iso were selected based on a comparison of a sample size corrected Aikake information criterion (AICc) and visual assessment of the conformity of model residuals to the assumptions of normality, homogeneity and the absence of undue influential observations. This model was subsequently re-fitted with the original unstandardised variables. The same approach was also applied to the 27 soils from the EUR sampling campaign and extended to consider the relationships with soil texture and carbon and nitrogen contents to investigate their utility in up-scaling efforts. To prevent over-fitting, these models were limited to a maximum of two predictive terms. The predictive terms considered were soil sand, silt, clay, carbon and nitrogen content, the ratio of carbon to nitrogen content and soil pH.

To investigate the influence of the NH₄NO₃ addition on k_iso, the variables of interest were expressed as the ratio of the mean of the soils that received an addition and that of their respective untreated counterparts with quotients smaller and greater than one, respectively, indicating a reduction and increase following addition. Correlations between these fractional changes for k_iso, microbial biomass, pH, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ were investigated through Spearman's rank correlation between pairs of variables. The minimal adequate, generalised linear model describing the fractional change in k_iso across these soils was investigated by comparing the AICc and visual inspection of the residuals for models that considered each independent variable separately to avoid over-fitting.

3.1 Variations among untreated soils

Clear differences in k_iso, pH, microbial biomass, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ were not apparent as a function of sampling site climatic zone or land cover (Fig. 2). Estimates of k_iso ranged from 0.01 to 0.40 s⁻¹, with the greatest rates occurring in soils sampled from hot-summer Mediterranean (Csa), hot semi-arid (Bsh) and subtropical (Cfa and Cwa) climates (Fig. 2a). Soil pH ranged from 3.9 to 8.6 and was mostly acidic or neutral, with alkaline conditions only found for soils sampled from hot-summer Mediterranean (Csa) and hot semi-arid (Bsh) climates (Fig. 2b). Ranging from 98.5 to 2898.1 µg C g dry soil⁻¹, microbial biomass did not appear to vary systematically with sampling site origin. Exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ ranged from 0.3 to 275.7 µg N g dry soil⁻¹ (Fig. 2d) and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ ranged from 2.5 to 64.7 µg N g dry soil⁻¹, with the greatest values found in soils sampled from temperate climates (Fig. 2e).

Figure 2Measurement summaries of mean untreated soils by the Köppen–Geiger climatic zone of the sampling site. The 27 sites in western Eurasia (EUR) were within subarctic (Dfc; n=6), temperate oceanic (Cfb; n=13), hot-summer Mediterranean (Csa; n=7) and hot semi-arid (Bsh; n=1) climate zones, and the 17 sites in northern Queensland, Australia (AUS), were within tropical monsoon (Am; n=3), humid subtropical (Cfa; n=9) and monsoon-influenced humid subtropical (Cwa; n=5) climate zones. Box lower, middle and upper hinges, respectively, indicate 0.25, 0.5 and 0.75 quantiles. Over-plotted points are the associated site means (n=2 or 3) with shape indicating land cover: (a) k_iso, (b) pH, (c) microbial biomass (MB), (d) exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$, and (d) exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$.

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Figure 3Observed (points) and modelled relationships following Eq. (6) (dashed lines) between the rate of oxygen isotope exchange (k_iso) and soil pH, exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and microbial biomass (MB): (a) the positive relationship between k_iso and soil pH with model response as a function of the shown range in soil pH calculated with median microbial biomass and lower quartile (green dashed line) and upper quartile (orange dashed line) exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$, (b) the negative relationship between k_iso and exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ with model response as a function of the shown range in exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ calculated with median microbial biomass and lower quartile (green dashed line) and upper quartile (orange dashed line) soil pH, and (c) the positive relationship between k_iso and microbial biomass with the model response as a function of the shown range in microbial biomass calculated with median exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and lower quartile (green dashed line) and upper quartile (orange dashed line) soil pH. Grey shaded areas indicate the 95 % confidence intervals associated with model fits.

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Individual relationships between pairs of these variables were investigated through Spearman's rank correlation (Table 1). Strong, significant correlations (p<0.05) were only found between k_iso and soil pH (Spearman's ρ=0.58), k_iso and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (Spearman's $\mathit{\rho }=-\mathrm{0.62}$) and soil pH and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (Spearman's $\mathit{\rho }=-\mathrm{0.73}$). Correlations between all other variable pairings were weaker and non-significant (p>0.05).

Table 1Spearman's rank correlation coefficients (ρ) for relationships between site mean oxygen isotope exchange rate (k_iso), soil pH, microbial biomass (MB), exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ measured in untreated soils (n=44).

^a indicates p<0.05 and ^b indicates p<0.01.

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Figure 4Rates of oxygen isotope exchange (k_iso) predicted by the minimal adequate statistical model identified (Eq. 6): (a) model predictions for the 44 untreated soils against the observations for these soils used in model fitting and (b) predicted fractional changes in kiso between treated and untreated soils against the changes observed following NH₄ NO₃ addition. Plotted points indicate individual sites with the associate sampling campaign indicated by colour (EUR: orange, AUS: green), dotted lines indicate the 1:1 line and dashed blue lines indicate linear relationships between predicted and observed values with a shaded 95 % confidence interval.

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Based on AICc and visual inspection of model fit and residuals (Fig. S2 in the Supplement), the structure of the generalised linear model describing variations in k_iso as the response variable was specified with a Gaussian error distribution and log–link function (Thomas et al., 2017). The minimal adequate model with this structure included the additive effects of soil pH, the natural logarithm of exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$, the natural logarithm of microbial biomass, the interaction between soil pH and the natural logarithm of exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and an intercept term (Fig. 3). This model explained 71 % of the deviance in k_iso (Fig. 4a) compared to the null model containing only an intercept term. Its AICc was 6.1 lower than the next best alternative model that omitted the interaction term, 7.1 lower than the closest model containing the sampling campaign and 13.3 lower than the closest model containing the natural logarithm of exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (Table S1 in the Supplement). The AICc values of single-term models containing only pH or the natural logarithms of microbial biomass or exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ were, respectively, 21.6, 43.6, and 50.2 greater than the best model. The selected model predicts the response variable, k_iso-pred (s⁻¹), in the original measurement units following Eq. (6):

where pH is soil pH, ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (µg N g dry soil⁻¹) and MB is microbial biomass (µg C g dry soil⁻¹). The model predicts that variations in k_iso result from positive correlations with soil pH (Fig. 3a) and microbial biomass (Fig. 3c) and negative correlation with exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$. The interaction between soil pH and exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is such that the negative influence of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ on k_iso occurs mainly under acidic conditions and is marginal at neutral to alkaline pH (Fig. 3b).

As with the full dataset, across the 27 soils from the EUR sampling campaign the strongest relationship describing k_iso was found with pH (Spearman's ρ=0.58), whilst a weaker but still significant (p<0.05) relationship with exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Spearman's $\mathit{\rho }=-\mathrm{0.42}$) was also identified. No significant (p>0.05) relationships between k_iso and clay (Spearman's ρ=0.11), silt (Spearman's $\mathit{\rho }=-\mathrm{0.18}$), sand (Spearman's ρ=0.00), carbon (Spearman's $\mathit{\rho }=-\mathrm{0.03}$) or nitrogen (Spearman's $\mathit{\rho }=-\mathrm{0.32}$) contents were found, whilst the relationship with the ratio of total carbon to nitrogen content (Spearman's ρ=0.38) was marginal (p=0.05). The minimal adequate generalised linear model (Table S2 in the Supplement) explaining variations in k_iso selected from only the relatively invariant properties of soil texture and carbon and nitrogen content included only the intercept (−2.128) and the effect of nitrogen content (−0.119). This model explained 11 % of the deviance in k_iso compared to the null model. After inclusion of soil pH, the minimal adequate model included the intercept (−4.535) and the additive effects of soil pH (0.4028) and clay content (−0.0017). This model explained 61 % of the deviance in k_iso compared to 54 % for the model containing only the intercept (−4.535) and influence of soil pH (0.339).

3.2 Variations induced by NH₄NO₃ addition

The addition of NH₄NO₃ systematically increased exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and decreased k_iso and soil pH. Exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ in the treated soils that received the NH₄NO₃ addition were, respectively, 1.9 to 173.6 and 3.7 to 18.8 times greater than in the corresponding untreated soils. Soil pH and k_iso were, respectively, 0.86 to 0.98 and 0.21 to 0.76 times smaller in the soils that received the addition compared with the corresponding untreated soils. The addition did not have a systematic influence on microbial biomass, which varied between 0.64 and 1.84 of the magnitude in the corresponding untreated soils. The absolute values of these changes are shown in Fig. S3 in the Supplement.

Table 2Spearman's rank correlation coefficients (ρ) for relationships between fractional changes in the mean rate of oxygen isotope exchange (k_iso), soil pH, microbial biomass (MB), exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and exchangeable ${\mathrm{NH}}_{\mathrm{4}}^{+}$ between soils receiving a NH₄NO₃ addition and that of the corresponding untreated soils (n=14).

^a indicates p<0.05 and ^b indicates p<0.01.

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Individual relationships between pairs of these fractional changes were investigated through Spearman's rank correlation (Table 2). Strong, significant correlations (p<0.05) for variable pairs were found between the fractional changes in k_iso and soil pH (Spearman's ρ=0.57), k_iso and exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Spearman's $\mathit{\rho }=-\mathrm{0.84}$) and soil pH and exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Spearman's $\mathit{\rho }=-\mathrm{0.75}$). Correlations between all other variable pairings were weaker and non-significant (p>0.05).

Figure 5Observed negative relationship between the fractional change in the rate of oxygen isotope exchange (k_iso) and the fractional change in exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ between treated and untreated soils following NH₄NO₃ addition for the 14 sites considered. Plotted points indicate the change for individual sites with the associate sampling campaign indicated by colour (EUR: orange, n=9; AUS: green, n=5). On the y axis, quotients below 1 indicate that k_iso in soils receiving the treatment decreased relative to corresponding untreated soils for each site. On the x axis, quotients above 1 indicate that ${\mathrm{NO}}_{\mathrm{3}}^{-}$ availability in soils receiving the treatment increased relative to corresponding untreated soils for each site. The blue dashed line shows the fit of the minimal adequate generalised linear model describing the change in k_iso with 95 % confidence intervals shaded in grey.

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Based on AICc and visual inspection of model fit and residuals, the structure of the generalised linear model describing variations in the fractional change in k_iso as the response variable was specified with a betareg error distribution and identity link function (Thomas et al., 2017). The minimal adequate, single-term model with this structure included the natural logarithm of the fractional change in exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (−0.499) and an intercept term (1.219). This model predicts the variations in the fractional change in k_iso following NH₄NO₃ addition across soils from the 14 sites' considered result from a negative relationship with fractional changes in exchangeable ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. 5). This relationship explained 76 % of the deviance in the fractional change in k_iso, and the model had an AICc that was 13.2 lower than the model that included the fractional change in soil pH and an intercept term (Table S3).