A common technique to quantitatively estimate P speciation in soil samples is to apply linear combination fitting (LCF) to normalized P K-edge X-ray absorption near-edge structure (XANES) spectra. Despite the rapid growth of such applications, the uncertainties of the fitted weights are still poorly known. Further, there are few reports to what extent the LCF standards represent unique end-members. Here, the co-variance between 34 standards was determined and their significance for LCF was discussed. We present a probabilistic approach for refining the calculation of LCF weights based on Latin hypercube sampling of normalized XANES spectra, where the contributions of energy calibration and normalization to fit uncertainty were considered. Many of the LCF standards, particularly within the same standard groups, were strongly correlated. This supports an approach in which the LCF standards are grouped. Moreover, adsorbed phytates and monetite were well described by other standards, which puts into question their use as end-members in LCF. Use of the probabilistic method resulted in uncertainties ranging from 2 to 11 percentage units. Uncertainties in the calibrated energy were important for the LCF weights, particularly for organic P, which changed with up to 2.7 percentage units per 0.01 eV error in energy. These results highlight the necessity of careful energy calibration and the use of frequent calibration checks. The probabilistic approach, in which at least 100 spectral variants are analyzed, improves our ability to identify the most likely P compounds present in a soil sample, and a procedure for this is suggested in the paper.

Summary The kinetics of orthophosphate (PO4) sorption in soil has far reaching consequences on its long‐term fate. Traditionally, a distinction is made between fast, reversible adsorption and slow fixation. The kinetics are commonly described by compartmental models (CMs) assuming kinetically distinct homogeneous pools (e.g. a rapid‐ and slow‐sorbing pool), with phenomenological equations or with complex diffusion‐based models. Alternatively, this process can be described by assuming frequency distributions of both adsorption and desorption rate constants and, thereby, enabling better description of experimental data with fewer adjustable parameters. Here, we developed such a rate constant distribution (RCD) model and compared it with CMs and other commonly used rate equations. Batch 33PO4 sorption was measured in agitated suspensions between 2 minutes and 20 days after spiking in 13 contrasting types of soil and two iron oxyhydroxides. Overall, the RCD model, with three adjustable parameters, describes the data better than the other models tested. The so‐called slow reactions, denoted as the factor change in soluble 33PO4 between 1 and 20 days after spiking, were described better by the RCD model and ranged from 1.0 (i.e. no change) to 6.9. The extent of slow reactions increased with the increase in the fraction of poorly crystalline iron in the soil (r = 0.69; P = 0.0088). Equilibrium was elusive up to 20 days for PO4 sorption on ferrihydrite and on soil samples with a large fraction of poorly crystalline iron oxyhydroxides. The RCD model code is available as freeware from the first author. Highlights A new rate constant distribution (RCD) model for PO4 sorption kinetics was developed. The RCD model offers a simple approach to take surface heterogeneity into account. The RCD model fitted PO4 sorption kinetics better than commonly used equations. Equilibrium was elusive for PO4 sorption on ferrihydrite and soil with poorly crystalline iron.

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To improve phosphorus (P) fertilization and environmental assessments, a better understanding of release kinetics of solid-phase P to soil solution is needed. In this study, Fe (hydr)oxide-coated filter papers (Fh papers), isotopic exchange kinetics (IEK) and chemical extractions were used to assess the sizes of fast and slowly desorbing P pools in the soils of six long-term Swedish field experiments. The P desorption data from the Fh-paper extraction of soil (20 days of continual P removal) were fitted with the Lookman two-compartment desorption model, which estimates the pools of fast (Q 1 ) and slowly (Q 2 ) desorbing P, and their desorption rates k 1 and k 2 . The amounts of isotope-exchangeable P (E) were calculated (E 1min to E >3 months ) and compared with Q 1 and Q 2 . The strongest relationship was found between E 1 min and Q 1 (r 2 = .87, p < .01). There was also an inverse relationship between the IEK parameter n (the rate of exchange) and k 1 (r 2 = .52, p < .01) and k 2 (r 2 = .52, p < .01), suggesting that a soil with a high value of n desorbs less P per time unit. The relationships between these results show that they deliver similar information, but both methods are hard to implement in routine analysis. However, Olsen-extractable P was similar in magnitude to Q 1 (P-Olsen = 1.1 × Q 1 + 2.3, r 2 = .96), n and k 1 were related to P-Olsen/P-CaCl 2 , while k 2 was related to P-oxalate/P-Olsen. Therefore, these extractions can be used to estimate the sizes and desorption rates of the different P pools, which could be important for assessments of plant availability and leaching.

The objective of this study was to understand how eight decades of tillage affected soil element dynamics. We measured soil chemical properties and the 14C:12C ratio (Δ14C) of organic carbon in one of the oldest cropland experiments in Europe with different levels of phosphorus addition. Soil total and organic phosphorus stocks in the uppermost 20 cm did not differ significantly between the control and the phosphorus addition treatments after 80 years, indicating plant phosphorus uptake from the subsoil. Crop yields increased from 220 g dry weight m−2 in 1936 to more than 500 g dry weight m−2 in the 2010s. The soil total organic carbon and total organic phosphorus stocks decreased by 13.7% and 11.6%, respectively, in the uppermost 20 cm of the soils during the experiment, irrespective of phosphorus addition. Based on modeling of Δ14C, we show that the mean transit time of carbon in the soil was below 10 years, indicating that a large share of the carbon inputs to soil is quickly respired. Our results suggest that the current agricultural practice at this long-term experiment is not sustainable because it led to a continuous decrease in soil organic matter over the last decades, despite increases in plant productivity.