3.1 Global analysis of P turnover in the soil solution (K_m)

The turnover rate of P in the soil solution ranged 9 orders of magnitude from 10⁻² to 10⁶ min⁻¹ across the 217 soils surveyed (Fig. 1). However, approximately half of the soils had a P turnover rate within the range of 10⁰ to 10² min⁻¹. Clear differences in K_m between different soil groups suggest that K_m is related to soil properties governing kinetics of inorganic P in the soil solution system. Surface soil horizons of Ferralsols had the highest values of K_m, followed by Andosols and Cambisols (Fig. 1). High K_m values of Ferralsols suggest that P in these soils is rapidly adsorbed, i.e., these soils have a high P-buffering capacity. Three of the four lowest K_m values were found in Podzols, soils which are known to have low P-sorbing capacity (Chen et al., 2003; Achat et al., 2009).

Figure 1Violin plots of P turnover (K_m) for different world reference base soil groups. Only soil groups with at least five observations were plotted. The number of observations in each violin is written next to the plot. Violin plots were made using the R package “vioplot” (Adler, 2005).

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Fardeau, Morel, and Boniface (Fardeau et al., 1991) showed that K_m is largest for small values of n and m, and becomes smaller as n approaches 0.5, and as m approaches 1. Values of n and m have often been found to correlate with soil properties (pH, carbonate concentration, oxalate-extractable Al/Fe, organic matter, etc.; Tran et al., 1988; Demaria et al., 2013; Frossard et al., 1993; Achat et al., 2013). A global compilation study showed that low values of n occur for soils with low concentrations of oxalate-extractable Al and Fe, which are indicative of amorphous Al and Fe oxides (Achat et al., 2016). In contrast, low values of m tend to occur for soils with a low ratio of organic C to Al and Fe oxides (Achat et al., 2016). The high K_m values of Ferralsols are due to extremely low m values (mean = 0.025, SD = 0.012, n= 26), and are consistent with low ratios of organic C to Al and Fe oxides typically reported in these soils (Randriamanantsoa et al., 2013). The Podzols in the data set, on the other hand, have distinguishably high m values (Mean = 0.50, SD = 0.43, n= 14), consistent with the low Al and Fe oxide content of the upper horizon of Podzols (Achat et al., 2009). However, small sample sizes per soil group and large spans in soil properties even within soil groups mean that group-specific K_m values should not be over-interpreted.

Figure 2Simple linear regression between soil solution P turnover (K_m) and soil solution P concentration (P_w) for 217 soils. The equation is given by $\log \mathrm{10}\left(K_{\mathrm{m}}\right)=\mathrm{1.26}-\mathrm{0.960}\times \log \mathrm{10}\left(P_w\right)$ with F= 127, p < 10⁻¹⁵, and R²= 0.37. Dashed lines represent the 95 % confidence interval.

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3.2 Relationship between soil solution P turnover (K_m) and concentration of soil solution P (P_w)

There was a negative correlation between K_m and P_w, as shown in Fig. (2) and described in Eq. (6):

with F= 127, p < 10⁻¹⁵, and R²= 0.37. The two variables P_w and K_m are important in governing plant-available P, because the former describes the amount of P in solution and the latter describes the rate at which it is exchanged. At t= 1 min, the highest values of E_(t) occurred for soils with high values of K_m and P_w, whereas the lowest values of E_(t) occurred for soils with low values of K_m and P_w (Fig. S1 in the Supplement). The relationship was less clear at t= 1 day (Fig. S1). However, the trend that lowest E values occurred for soils with a low K_m and low P_w is still apparent at t= 1 day.

Figure 3Soil solution P turnover (K_m) as a driver of available P (E_(t)). While there is a large range in P availability at t= 0 (P_w), this variability becomes smaller and gradually uncoupled from P_w class for longer time frames (t= 1, 1440, 129 600 min a). The growth in P availability between t= 0 and t= 1 is dependent on K_m (b). Simple linear regression between K_m and the difference between E₍₁₎ and E₍₀₎ is given by $\log \mathrm{10}\left(E_{\left(\mathrm{1}\right)}\right)-\log \mathrm{10}\left(E_{\left(\mathrm{0}\right)}\right)=\mathrm{0.170}+\mathrm{0.357}\times \log \mathrm{10}\left(K_{\mathrm{m}}\right)$ with F = 615, p < 10⁻¹⁵, and R²= 0.79. n= 170. Red, orange, and green colors refer to classes of low, middle, and high P_w as determined by Jenks natural breaks optimization. In (b), dashed lines represent the 95 % confidence interval.

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The negative correlation between K_m and P_w confirms our second hypothesis, that soils with high P_w would have low K_m, and is in accordance with findings from other studies using different methodological approaches. For example, it has been observed that sorption is less pronounced on heavily fertilized soils, due to more negative surface charge (Barrow and Debnath, 2014). In our study, high K_m values imply the presence of many potential binding sites, where P may adsorb or precipitate. This leads to a rapid exchange between sorption sites and the soil solution, as solution P quickly binds to a new site. Consequently, P_w is low. On the other hand, slower turnover rates of P in the soil solution and high P_w occur when P-binding sites are few or saturated.

3.3 Soil solution P turnover (K_m) as a buffer of isotopically exchangeable P (E_(t))

We found that K_m is an important buffer of isotopically exchangeable P. As t increases, E_(t) values diverge from P_w and eventually approach P_inorg. Interestingly, the range of E_(t) values decreased with time (Fig. 3a). While P_w values ranged almost 4 orders of magnitude, E₍₁₎ values only ranged 3 orders of magnitude. Furthermore, differences in E values among soils of low, middle, and high P_w decreased with time. We found that the difference between log₁₀(E₍₁₎) and log₁₀(E₍₀₎) was strongly correlated with log10(K_m) (F= 615, p < 10⁻¹⁵, and R²= 0.79). Thus, soils with fast rates of K_m had large increases in E_(t) compared to soils with slow rates of K_m, which showed little difference in E_(t) from E₍₀₎ to E₍₁₎. Furthermore, soils with the largest increases in E_(t) had low concentrations of P_w but high values of K_m (Fig. 3b).

While it is evident that E_(t) and K_m are related since both variables are calculated from the same isotope exchange kinetic parameters, the dependency reveals that many soils with low concentrations of P_w attained E values comparable to other soils due to extremely high soil solution P turnover rates (Fig. 3b). One can thus interpret that a soil with high K_m has a higher PBC and that a majority of P applied as fertilizer will be quickly adsorbed. On the other hand, high turnover means that there is a large flux of P ions through the soil solution, and phosphate ions in solution are quickly replaced through desorption when plants take up P. If soils with E_(1min) value of over 5 mg P kg⁻¹ are considered highly P fertile (Gallet et al., 2003), high P fertility can be found in both soils with high P_w and/or soils with low P_w but high K_m (Fig. S1). Soils with low P_w and low K_m, such as most Lixisols, also have low E values. Thus, P fixing by soils is reversible and says little about P availability.

Figure 4R² of simple linear regressions between isotopically exchangeable P (E_(t)) explained by predictors P_w (a), K_m (b), and P_inorg (c) as a function of time. Regressions were fit separately for each class of P_w (low, middle, high), as determined by Jenks natural breaks optimization. Low P_w= 0.008–0.16 mg kg⁻¹ (n= 46), middle P_w= 0.16–1.9 mg kg⁻¹ (n= 94), and high P_w= 1.9–42.5 mg kg⁻¹ (n= 77).

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3.4 Time frame over which K_m buffers isotopically exchangeable P (E_(t))

On which time frame is E_(t) dependent on K_m? By performing linear regressions among P_w, K_m, and P_inorg, respectively, and E_(t) for t= 1 min to 3 months, we found that the fits are strongly dependent on P_w class (high, middle, low). Based on Jenks natural breaks optimization, three clusters of P_w were determined: 0.008–0.16 (n= 46), 0.16–1.9 (n= 94), and 1.9–42.5 mg kg⁻¹ (n= 77). Calculating the R² of the regression as a function of time showed that for the class of high-P_w soils, P_w explained 60 % of variability in E_(t) at 1 min (Fig. 4a). However, P_w lost power as a predictor of E_(t) rapidly, explaining only 20 % of variability by t= 60 min. In contrast, soils with low concentrations of P_w showed no relationship between values of E_(t) and P_w even at short time spans. Thus, the concentration of P in the soil solution has a strong legacy on plant P availability for soils with high P_w at short time spans, but does not indicate P availability in soils with low concentrations of P_w. In these soils, values of E_(t) are primarily driven by K_m (Fig. 4b). Eventually both K_m and P_w lose predictive power, as E_(t) inevitably approaches P_inorg (see Eq. 4; Fig. 4c). However, predictive power of P_inorg is again dependent on P_w class.

E_(t) over time spans between 1 min and 3 months were differently related to predictors P_w, K_m, and P_inorg depending on concentrations of P_w. The effect of K_m on E_(t) is thus strongly dependent on P_w. In P-depleted soils the kinetic component is crucial in predicting a soil's P availability. An underestimation of the kinetic components of P availability will lead to over-fertilization of P-fixing soils. In more P-rich soils, however, P availability can be relatively accurately assessed with static measures, i.e., the concentration of P in the solution and the total inorganic P in the soil.

Figure 5Simple linear regression between phosphorus-buffering capacity (PBC) and soil solution P turnover (K_m) for 18 long-term P fertilizer experiments. PBC was calculated as the slope of the regression between P_w and P budget. PBC was found to correlate with K_m, as given by $\log \mathrm{10}\left(\mathrm{PBC}\right)=-\mathrm{0.481}-\mathrm{0.482}\times \log \mathrm{10}\left(K_{\mathrm{m}}\right)$, with R² of 0.40 (F= 10.8, p= 0.0047). Dashed lines represent 95 % confidence interval.

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3.5 K_m buffers fertilizer application in long-term fertilizer experiments

There was a positive relationship between P_w and P budget across all 18 long-term P fertilizer experimental sites, which is consistent with the study of Morel et al. (2000). However, the slopes spanned 3 orders of magnitude, from 0.007 (mg P kg⁻¹ soil)∕(kg P ha⁻¹ yr⁻¹; Ferralsol, Colombia; Oberson et al., 1999) to 3.9 (mg P kg⁻¹ soil)∕(kg P ha⁻¹ yr⁻¹; Chernozem, Canada; Morel et al., 1994). This shows that soil solution P is more strongly buffered in some soils than others. Results from the fertilizer experiments thus confirm that in high P-sorbing soils, such as Ferralsols, additions of P fertilizers may lead to only incremental increases in solution P concentration (Roy et al., 2016). However, this does not necessarily translate to P availability (Pypers et al., 2006).

PBC on the field experiments, taken as the slope of P_w increase with increasing P budget, was negatively dependent on K_m (F= 10.8, p= 0.0047, and R²= 0.40; Fig. 5). In other words, soils with higher K_m values were characterized by slower increases in P_w at similar yearly P input–output budgets, and vice versa. Both PBC and K_m are measures which describe the exchange of P between the soil solution and solid phases (Olsen and Khasawneh, 1980; Fardeau et al., 1991). However, the two have never been directly related. Data from long-term field experiments enabled us to compare K_m to field-scale PBC. The fact that the two are correlated in fertilizer field experiments thus underlines our findings from the global soil investigation that K_m and PBC provide information on the same underlying processes.

Figure 6Relative standard deviations (RSDs) of K_m after error propagation assuming 10 % uncertainty in m and n input parameters. The plot shows the m and n values from the 217 soils included in this global compilation study. Uncertainty in K_m was approximated using the partial derivatives approach. Bubble size and color relates to the RSD of K_m for the plotted m and n combination.

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3.6 Implications for using K_m

Most previous studies involving isotopic exchange kinetics have focused on analyzing m, n, and E values (Frossard et al., 1993; Achat et al., 2016; Tran et al., 1988; Brédoire et al., 2016). However, m and n are simply statistical parameters, whereas K_m can be readily interpreted in terms of soil processes (Fardeau et al., 1991). K_m is the mechanism behind PBC and is useful in explaining P availability. However, when using K_m, it is important to be aware of its limitations (as described in the methods section) and its sensitivity to the parameters m and n. (Fig. 6) Depending on the study, a relatively large uncertainty for K_m may be acceptable because differences in K_m between soils or treatments often vary on orders of magnitude (Frossard et al., 2011; Fardeau et al., 1991). However, for low values of m and/or n, K_m calculation becomes very sensitive to uncertainty in m and/or n, and relative errors may be much higher than 100 % (Fig. 6). Future studies should take this into account and conduct appropriate error propagation, or consult Fig. 6 to get an overview of sensitive m and n ranges.

While we focused our analysis on P studies, the derivation of K_m as well as the finding that there is extremely rapid exchange between solid and liquid phases is equally relevant for other nutrients and/or pollutants with strongly sorbing ion species. The isotope exchange kinetic approach has also been successfully applied to study availability of Zn (Sinaj et al., 1999), Cd (Gray et al., 2004; Gérard et al., 2000), Ni (Echevarria et al., 1998), As (Rahman et al., 2017), and U (Clark et al., 2011), and applications are also plausible for other elements with radioisotopes. Isotope exchange kinetic studies with Zn, Cd, and Ni have used the same method as studies on P analyzed here, also modeling the decline in radioactivity using Eq. (3; Gray et al., 2004; Sinaj et al., 1999; Echevarria et al., 1998). For such studies, the derivation of K_m as it is presented here is directly transferable and might provide additional useful information for understanding soil–solution exchange.

3.7 Environmental implications

Our study provides new insight into the diffusion-based mechanisms of P buffering across a large range of soil types. Prior to this study, little was known about soil solution P turnover rate, as K_m had previously been calculated by only a handful of studies. Our analysis of 217 soils showed that K_m is inversely proportional to P_w and is an important determinant of plant-available P. Biological adaptations to P availability have received a lot of attention, as it has been shown that plant communities have different strategies for P nutrition depending on P availability (Lambers et al., 2008). Indeed, biological activity acts as an important buffer of P availability in many ecosystems, with higher fluxes of biological P often occurring when there are lower fluxes of physicochemical P (Bünemann et al., 2016, 2012). Our global compilation of 217 samples demonstrated there is another buffer of soil solution P, which is independent of biological activity and exclusively diffusion-based. Soils with a low concentration of P in the soil solution tend to have a high P turnover rate, thus buffering isotopically exchangeable P values. This does not mean that negative balances of P will improve the availability of soil P for plant uptake, rather it explains why changes in P availability are not as large as suggested by more drastic changes in P_w.

Our findings complement the notion that there are two categories of soils in regard to P dynamics. In many low-P_w soils, sorption is extremely high and the soil solution is buffered from P inputs or outputs (Barrow and Debnath, 2014). For these soils, the prevalence of sites with fast exchange rates is crucial to assure a steady flux of P to the soil solution (Fig. 3b). In terms of agricultural management, in such a soil, P fertilization has to be higher than P output via crop removal to account for the buffering effect (Roy et al., 2016). However, once a soil reaches a certain P level and binding sites are saturated by phosphate and other anions, P exchange is less important and fertilizer inputs can be lowered to equal crop offtake (Syers et al., 2008). For these soils, additional P inputs will be directly reflected by an increase in P in the soil solution, and P availability is largely driven by the amount of P in the soil solution (Fig. 4a). A better understanding of P kinetics in soil will allow more effective nutrient management to meet the dual goals of improving agricultural production while reducing fertilizer use and pollution.