Background

Per- and polyfluoroalkyl substances (PFAS) are anthropogenic substances, which were created and used for products such as Teflon [1]. Currently, about 10,776 PFAS [2] are known, with a rapidly growing trend. While there are many useful fields of applications for PFAS, studies have already identified adverse effects associated with some PFAS, including persistence, bioaccumulation, and toxicity [3]. These effects vary within the group of PFAS, with most compounds not yet been investigated, as research has primarily focused on a few compounds [4]. This includes, for example, perfluorooctanoic acid (PFOA), which is classified as a persistent compound within the subgroup of perfluoroalkyl acids (PFAA) [5]. PFAA are final transformation products of various biotransformable PFAS, referred as precursors [6]. These precursors include the group of polyfluoroalkyl phosphate diesters (diPAP). 6:2 and 8:2 diPAP [7], two important representatives of this group, are focused in the present study, simulating their biotransformation and leaching of transformation products in soil.

DiPAPs are used in the paper industry as grease and water repellent agents [8] and have already been detected in various environmental compartments such as soils [9], lakes [10] and indoor dust [11]. Once diPAPs are present in the soil, they are rather immobile due to their high sorption potential, but continue to release their transformation products [7]. PFAA, the mobile final transformation products of 6:2 diPAP and 8:2 diPAP [7], can rapidly enter the food web through plant uptake [12] or leach into groundwater [13], which may be a problem for several decades [14].

Due to the extensive range of PFAS and their diverse properties, there are currently gaps in our knowledge, particularly concerning the behavior of PFAS in the vadose zone. Studies involving non-degradable PFAS have shown that they exhibit lower recovery rates as the chain length increases [7, 15]. This phenomenon is often attributed to non-extractable residues (NER) [7], “irreversible sorption” [16] or “immobilized” compounds [15], all of which essentially have similar meanings. It has been established for other substances that they can form NER in soil through various mechanisms [17]. Although the process is not well understood, it has been frequently cited as a potential cause for a mass balance gap of PFAS in soil environments [7, 18, 19]. Several studies have also investigated the sorption of PFAS in soil. Fabregat-Palau et al. [20] attempted to estimate a sorption coefficient based on soil composition and chain length for a few PFAA but with significant uncertainties. Therefore, the estimate can only serve as an initial approximation due to the multitude of influencing factors. The study highlighted that the organic carbon content and the mineral soil fraction (clay and silt) have an impact on sorption, in addition to compound properties. However, the influence of these factors can vary depending on other parameters, such as the presence of other organic compounds or ions [21]. Understanding NER formation and sorption is crucial for estimating the potential of PFAS release from NER into soil.

The transformation pathways of certain precursors have been studied and documented [19, 22, 23]. However, transformation rates are often determined under constant environmental conditions [7, 19] and, in some cases, based on only two data points, assuming a uniform transformation rate [7, 12, 24]. It is important to note that transformation rates can be influenced by various factors. Firstly, the NER fraction may increase over time due to soil aging effects, as described in Cheng et al. [25] for organic pollutants. Consequently, the fraction of precursor available for transformation may decrease over time. Secondly, if microorganisms are involved in the transformation process, as observed in the transformation of diPAPs [19], parameters that influence microbial productivity also affect the transformation rate. These parameters include temperature [26, 27], oxygen availability [26, 27], soil water content [28, 29], the ability of plants to influence microbial communities [30], the strains of microorganism [31] and their environmental preferences, and the availability of nutrients [26, 27]. These diverse factors highlight the need to investigate their impact on precursor transformation to better predict the variability of transformation rates. Understanding these influencing factors can be used to model precursor transformation, enabling better estimations of substance behavior in contaminated soils.

Various models are available for simulating transformation and leaching processes in the vadose zone. These models were initially developed for pesticide registration purposes [32], but have been applied to other substances as well. Examples of such applications include veterinary antibiotics [33], pharmaceuticals [34] and nutrients [35]. Simulation studies involving different PFAS, primarily non-degradable ones [36], have also been conducted using various models such as HYDRUS [37] and MACRO [38]. These studies have examined environmental conditions such including saturated [39, 40] and unsaturated soils [18, 37, 38, 41], laboratory settings [41] and field conditions [18, 38]. Additionally, they have investigated various processes such as NER formation [38] and sorption at the air–water interface [37]. In existing models processes are limited to the leaching of PFAA [18, 37,38,39, 41,42,43], transformation of diPAP and leaching of PFAA [41], the transformation of PAP [19], the uptake of PFAA in plants [44] and the behavior in the saturated zone [39, 42, 43, 45]. Additionally, a further overview is given in [36].

Available simulation studies focusing on precursor transformation in the vadose zone have primarily focused on areas contaminated with Aqueous Film-Forming Foam (AFFF) [46, 47]. However, a laboratory-based simulation study using unsaturated soil columns has been conducted to investigate the transformation of 6:2 and 8:2 diPAP [41]. The results of this study revealed that the biotransformation rate was not constant, indicating that changing conditions such as soil water content and oxygen availability influenced the transformation process.

In the present simulation study, we aimed to simulate the transformation of 6:2 diPAP and 8:2 diPAP, as well as related processes such as substance leaching, sorption and plant uptake, using data from a lysimeter study [24]. To the best of our knowledge, there is currently no existing simulation study that specifically addresses the transformation, leaching and plant uptake of transformation products of diPAPs and diPAPs in the vadose zone under near-natural conditions.

Materials and methods

Lysimeter study

In the 2-year lysimeter study in Schmallenberg, Germany [24], four lysimeters were set up to investigate the behavior of 6:2 and 8:2 diPAP individually in a duplicate setup each. The target concentration of diPAPs were 2 mg/kg dry matter for the upper soil half, having a total input mass of 628.5 mg in each lysimeter, which corresponds to a molar amount of 0.80 mmol (6:2 diPAP) and 0.63 mmol (8:2 diPAP). To prevent erosion, grass was planted on the surface of the lysimeters. The lysimeters were exposed to natural climate conditions and were not artificially watered.

Throughout the study, samples of percolate were collected at irregular intervals from the bottom of the lysimeters at 65 cm. The topsoil includes the soil until a depth of 25 cm, the subsoil the depth from 25 cm down to 60 cm and a gravel layer was added from a depth of 60 cm down to 65 cm. Grass samples were collected each year, and soil samples were obtained from five different depths at the end of study. Two methods were used to quantify PFAS, with detailed information provided in the original article [24]. The results presented in the study focus on the target method using tetrabutylammonium hydrogensulfate to quantify individual PFAS masses.

For the simulation study, values given in [24] are converted from concentrations to masses. All used values are listed in Additional file 1: Tables S3–8 in the supporting information, as well as an overview of the mass balance is shown in Additional file 1: Fig. S1.

The MACRO model

MACRO is a 1D numerical model used for simulating solute transport and water flow in the vadose zone [48]. Originally developed for pesticide registration procedures, MACRO has been adapted for studying various substances [33, 38]. In this simulation study, MACRO version 5.2 is used in the command line version, and parameter changes are controlled using GNU R. The macroutils package (version 1.15.0), recommended by MACRO developers [49], is employed to convert simulation results.

The model incorporates several key features that are relevant to the present study. The actual evapotranspiration is calculated based on input data of temperature and potential evapotranspiration. The potential evapotranspiration is partitioned into potential transpiration and potential evaporation via calculation of a fraction intercepted by the transpiring canopy surfaces and by dead plant material as well as a fraction which reaches the soil surface, respectively [50]. Both fractions are calculated using values of (green) leaf area index [50]. The actual evaporation is calculated with the value of potential evapotranspiration and the actual transpiration is calculated by using a function of the water stress index accounting for the water content and the distribution of roots [48].

Water flow and substance transport are simulated using two dual-permeable domains: micropores and macropores. Solute transport is influenced by various substance parameters, including the sorption coefficient KD, the linearity of sorption described by the Freundlich n parameter, anionic exclusion θAE, and transformation in all four domains (liquid/solid phase of micro-/macropores). Solute parameters can be adjusted individually for each soil horizon.

The actual transformation rate μD of the substances is calculated by

$$\mu_D \; = \;\mu_{{\text{ref}},D} \cdot F_w \cdot F_t ,$$
(1)

using the reference transformation rate μref,D and factors depending on temperature Ft and soil water content Fw. The factor Ft, which represents the influence of temperature on the transformation rate, is calculated using a three-section defined function:

$$F_t = e^{\alpha (T - T_{{\text{ref}}} )} \;{\text{with}}\;T > 5\;{^\circ} {\text{C}},$$
(2)
$$F_t = \left( \frac{T}{5} \right)e^{\alpha (5 - T_{ref} )} \;{\text{with}}\;0 \le T \le 5\; {^\circ}{\text{C}},$$
(3)
$$F_t = 0\;{\text{with}}\;T < 0\; {^\circ}{\text{C}}.$$
(4)

The function takes into account the reference temperature Tref at which the transformation rate μref,D was measured, the current temperature T and a parameter α. The default value of α is 0.08 (–) on the basis of Boesten, Linden [51]. Setting α to zero removes the temperature effect, while higher values of α amplify the impact of temperature on the transformation rate.

The factor Fw was updated from MACRO version 5.0 to 5.2 [52], using a different approach based on the work of Schroll et al. [53]. Fw is defined as a three-section function that depends on the current soil water content θ:

$$F_w = \;0\;{\text{with}}\;\theta \; < \;0.5\theta_w ,$$
(5)
$$F_w \; = \;\left( {\frac{\theta \; - \;0.5\theta_w}{{\theta_{100}\; - \;0.5\theta_w}}} \right)^B \;{\text{with}}\;0.5\theta_w \; < \;\theta \; < \;\theta_{100} ,$$
(6)
$$F_t = \, 1\;{\text{with}}\;\theta \; > \;\theta_{100} .$$
(7)

In very dry conditions, well below the soil water content at wilting point θw, the transformation rate is set to zero (5). As the soil water content increases until a water content corresponding to a pressure head of −100 cm is reached θ100, Fw can have values between 0 and 1 (6). In very moist conditions (7), the conditions are considered ideal, and Fw is set to 1, which is the maximum value. The parameter B can be set to zero to eliminate the influence of Fw, provided that the soil water content does not fall within the range described by Eq. (5).

MACRO does not have explicit built-in support for modeling NER. However, a possible workaround has been used in previous simulations [33, 38], where NER were modeled by using the transformation rate in the solid phase of the micropores.

Plant uptake Uc is calculated by

$$U_c \; = f_c \cdot S_r \cdot c^{\prime},$$
(8)

multiplying the solute concentration factor of the transpiration stream fc, the root water uptake volume Sr and the solute concentration c’.

Model parameterization

In the MACRO model, a free flow situation at the bottom outlet and a variable water input by precipitation was chosen as boundary conditions. Precipitation and temperature data were obtained from a weather station situated at the lysimeter site. In cases of missing data, nearby weather stations were utilized as substitutes. Daily potential evapotranspiration was derived from raster data provided by the DWD (German Weather Service) [54]. Obtained raster data were calculated by DWD on the basis of the agrometeorological model AMBAV (Agricultural meteorological calculation of the current evaporation) for weather stations since 1991 and a multiple linear regression [55]. The grass was simulated as an annual crop using estimated parameter values (Additional file 1: Table S11). Physical soil data were measured (Additional file 1: Table S1). Soil parameters were calculated using the pedotransfer function FOOTPRINT, which is part of the MACRO software. Initial soil water content and a selection of soil parameters were employed to calibrate the water flow (see Additional file 1: Table S9). Substance parameters used for optimizing the solute transport can be found in Table 1 and cover the KD value, anion exclusion θAE, Freundlich n and the NER rate \(\mu\) ref,s,mi. The parameters were varied for the two main transformation products of 6:2 diPAP perfluoropentanoic acid (PFPeA) and perfluorohexanoic acid (PFHxA) and the two main transformation products of 8:2 diPAP perfluoroheptanoic acid (PFHpA) and perfluorooctanoic acid (PFOA). All four transformation products belong to the group of the perfluorocarboxylic acids (PFCA), which belong to the PFAA group, and will be abbreviated with PFCA’, if they emerged from a precursor. The KD value was the only substance parameter which was varied for upper and lower soil separately, to reduce the amount of parameters within the optimization. The solute concentration factor fc was calibrated using the entire interval from 0 up to 1 (see Table 1).

Table 1 Substance related parameter used for optimization. n.d. not determined
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Initial diPAP masses in soil were set to recovered masses of the lysimeter study [24]: 401.9 mg and 522.7 mg for 6:2 diPAP and 8:2 diPAP, respectively, including their transformation products. The original mass input into the lysimeter for each compound was 628.5 mg. This approach was adopted due to uncertainties regarding the fate of the not recovered masses of precursors. NER were only simulated for PFOA, because of results given in [41]. The transformed masses were divided into multiple transformation products based on the formation fractions (ff) provided in Table 2. Formation fractions were determined using the amount of substance (mol), considering that two molecules of PFCA are equivalent to one molecule of diPAP [56]:

$$\it {\text{ff = }}\frac{{m_{PFCA^{\prime}} }}{{m_{diPAP^{\prime}} }}.$$
(9)
Table 2 Formation fraction values used in the model
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It was observed that under sterile conditions, there was hardly any degradation of diPAPs [19], indicating the likely influence of temperature and moisture content, as they have a demonstrable impact on microorganisms [57]. So, the approach followed here considers the degradation rate being influenced by temperature and moisture content, which is also similar to pesticides [57]. For the gravel layer no sorption and no degradation was assumed.

Evaluation of model performance and modeling strategy

Goodness-of-fit values

The Kling–Gupta efficiency KGE [58] is calculated by

$$\it {\text{KGE}}_x { = 1} - { }\sqrt {{\left( {r_x - {1}} \right)^2 + \left( {\alpha - {1}} \right)^2 + \left( {\beta - {1}} \right)^2 }} ,$$
(10)
$${\text{with}}\;\alpha { = }\frac{{s_x {\text{(m)}}}}{{s_x {\text{(o)}}}},\;\beta { = }\frac{{\overline{m_x }}}{{\overline{o_x }}},$$
(11)

using the Pearson correlation coefficient between simulated and observed values rx, a quotient of standard deviations sx, the average of simulated values \({\overline{m}_{x}}\) and the observed values \( {\overline{o}_{x}}\).

The root mean square error RMSE is calculated by

$$\it {\text{RMSE = }}\left( {\frac{1}{n}\mathop \sum \limits_{t = 1}^{ n} (m_t - o_t )^2 } \right){ }^{1/2} ,$$
(12)

using modeled values mt and observed values ot to create a mean absolute deviation of modeled values. For both objectives (KGE, RMSE), the hydroGOF (0.4–0) package was used.

Modeling strategy

The optimization was performed using the caRamel evolutionary algorithm [59] and 10,000 simulation runs. The transformation rate was influenced by both soil temperature and water content as described by Eq. (1). In each simulation run (Fig. 1), a parameter set was used, which included the soil parameters Van Genuchten’s alpha (0.02–1 cm−1), saturated hydraulic conductivity (50–150 mm h−1), initial volumetric soil water content of subsoil and topsoil (20–25%), as well as substance parameters of diPAP and PFAA transformation products (see Table 1).

Fig. 1
figure 1

Schematic of modeling strategy with 8:2 diPAP as example

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A modeling run was started using only soil parameters, soil water content and substance parameters of diPAPs. The results of this simulation as well as the substance parameters of the first transformation product were then used to simulate the leaching of the first transformation product, which was PFHpA in case of 8:2 diPAP. The same was done for the second transformation product PFOA. After a complete simulation, obtained values were compared to measured values via an objective function. The same was done for 6:2 diPAP and its transformation products. To evaluate the performance of each simulation run, four objectives were used. The KGE (9) was employed to evaluate the water flow and the RMSE was used to evaluate both transformation product masses observed in the percolate. Additionally, a simple difference between the observed and modeled values was minimized to assess the transformed diPAP mass. The optimization algorithm used the evaluation of these objective functions to create new parameter sets for subsequent simulation runs, aiming to improve the agreement between the model predictions and observed data.

After a complete optimization process, the simulations included in the Pareto front (best 500 and then 90%-quartile of every of the four objectives) were selected for the calibration of the plant uptake of PFAA transformation products. This calibration process was separated from the optimization process and involved adjusting the solute concentration factor fc. To calibrate fc, the interval bisection method was used. This method involves iteratively adjusting the factor fc within an interval and evaluating the goodness-of-fit with the observed data until the deviation from the observed values was less than or equal to 1%. The mean deviation of the substance uptake by plants for both years was used as a measure of the goodness-of-fit.

Results and discussion

Simulation results

The result of the optimizations were 314 simulations (6:2 diPAP) and 313 simulations (8:2 diPAP), that met the previously defined criteria. The water flow could be reproduced with good quality measures (KGE6:2 diPAP = 0.78–0.86, KGE8:2 diPAP = 0.85–0.86). This provided a solid foundation for simulating substance leaching. It is important to note that results obtained in controlled laboratory environments, such as the soil column study, may differ from natural conditions due to fewer variations in environmental factors like temperature and precipitation.

PFAS in percolate

In Fig. 2 the results of all chosen transformation product simulations in the period of April 2019 until April 2021 are shown. Until April 2020, all peaks and almost all observed values are covered by the simulations. Especially leaching dynamics of PFHpA and PFOA are well represented with only little deviations. Regarding PFPeA and PFHxA the dynamics are well represented as well, but wide simulation ranges are notable, which could be related to variations in the modeled values of water fluxes (see Additional files 1: Fig. S2). The variations between modeled and observed percolate were also found for 8:2 diPAP lysimeters, but the influence of the variation may have been higher on the more mobile PFPeA and PFHxA. An overestimation of 6:2 diPAP transformation products masses (see Fig. 3) also influenced the leaching of both substances.

Fig. 2
figure 2

Observed and modeled values of transformation products leaching of 6:2 diPAP (PFPeA, PFHxA) and 8:2 diPAP (PFHpA, PFOA) in mg/interval

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Fig. 3
figure 3

Observed and modeled values of 6:2 diPAP and 8:2 diPAP and transformation products of 6:2 diPAP (PFPeA, PFHxA) and 8:2 diPAP (PFHpA, PFOA) in mg/soil layer. The order is from topsoil (1) to subsoil (5)

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PFAS in soil

The modeling of the amount of diPAP, which is still adsorbed to soil particles, and its transformation products (PFPeA, PFHxA, PFHpA, PFOA), as shown in Fig. 3, was well-matched by the model, especially the dynamics with soil depth. Observed values of diPAPs in soil layers were all in the range of simulated values.

The best compromise overestimated the transformed amount of 6:2 diPAP. A high uncertainty of values can be found for the transformation products of 6:2 diPAP, PFPeA and PFHxA, although observed values are all within modeled ranges. The high uncertainty was only found in the upper two soil layers, whereby only outliers were recognized in the lower soil layers. This might be connected, to the simulations runs, in which transformed 6:2 diPAP mass was overestimated, or simulation runs, in which the highest KD-values were used for a better representation of leaching from the bottom layer.

The transformed masses of 8:2 diPAP were underestimated in the simulation of the best compromise for the two upper soil layers. The amount in the third layer of 8:2 diPAP was highly underestimated, which could be the result of the third layer being the transition layer from initially contaminated soil to uncontaminated soil. Adsorption masses of PFHpA were underestimated in the upper two soil layers and overestimated in the lower soil layers. PFOA was also underestimated in every soil layer, but the increasing dynamic with soil depth was well simulated. Changing soil parameters may not have been expedient, because PFHpA masses were overestimated and PFOA masses underestimated. An improvement of one value would have worsened the fitting of other values, which is already covered by the pareto front of the optimization algorithm. A variation of the ff value might have improved the simulation results, which was not done due to the availability of the measured value. But the underestimation of simulated transformed 8:2 diPAP, would have been compensated by increasing the ff value of PFHpA and PFOA.

Plant uptake of PFAS

The decreasing uptake of PFPeA and PFHxA in the grass from 2019 to 2020 and the magnitudes were well represented by the model (Fig. 4): The best compromises have only slight deviations from the observed values and the distribution of values was broad, but still in the same order of magnitude. However, observed uptakes of PFHpA and PFOA were similar for both years, but were also represented by a decrease in the model, resulting in an underestimation of values in 2020 and an overestimation for PFHpA in 2019. One reason for the decreasing uptake in the model could be a decreasing availability of substance in the soil, since the amount of precursor also decreased over time. Further, the water content in the soil was lower in 2020 due to lower precipitation than in 2019. A comparison of the vegetation period April to August shows a difference of 122 L/m2 (2019: 325 L/m2, 2020: 204 L/m2). Looking into air temperature (26.04.–31.08), both years were similar, with 2020 being slightly colder (2019: Tmean = 13.4 °C, standard deviation = 5.7 °C; 2020: Tmean = 13.0 °C, standard deviation = 4.7 °C). A lower soil water content could have influenced the transformation rate as well as the availability of substances for the grass. The question arises why this dynamic cannot be found for PFHpA and PFOA. In 2019 an overestimation and in 2020 an underestimation of simulated values can be found (Fig. 4). In case of simulated uptake values in 2019, an overestimation of transformed PFOA und PFHpA as well as their precursor 8:2 diPAP in the upper soil is likely the reason for an overestimated uptake. In case of 2020, the underestimation of simulated PFHpA and PFOA masses in the upper soil at the end of experiment might the reason, assuming a similar underestimation was also found before the vegetation period.

Fig. 4
figure 4

Observed and modeled plant uptake of 6:2 diPAP and 8:2 diPAP and transformation products PFPeA, PFHxA (6:2 diPAP) and PFHpA, PFOA (8:2 diPAP) in mg/year

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Parameter distribution

The optimized ranges and the initial ranges of substance parameters are given in Table 3 and Table 4 and in Additional file 1: Table S14–17. Although the initial parameter range was the same for all soil layers, the optimization found the substances more adsorptive to the upper soil layers (Additional file 1: Table S1), which are in fact more sorptive due to higher organic carbon content and mineral content (clay and silt). The upper boundaries of the parameter ranges were approached in several cases. An adjustment of the parameter ranges would have been a possibility, but was not done following the modeling strategy. Noticeable are the extreme differences of subsoil KD-values for both diPAP. The high ranges of KD values can be explained by a correlation to the degradation rate and the Freundlich n. The datapoint of diPAP masses in the third soil layer, which is the transition layer between upper and lower soil, is the only datapoint available to calibrate diPAP parameters for lower soil, which results in a high uncertainty in the found parameter values. Compared with another modeling study [41], optimized values of KD are higher for all PFAA in this study. The transport could be enhanced by different study conditions: in the present study, PFAA were slowly produced over time and in the comparing study, they were applied as a mixture on the soil surface, having more adsorption competition. A comparison of the optimized KD values of PFAA and literature, where upper and lower soil was comparable to this study [18], show that the modeled range fits the magnitude of the measured values quite well, supporting the results of the optimization.

Table 3 Initial parameter ranges and posterior parameter statistics of degradation rate \(\mu\) ref,l,mi and NER formation \(\mu\) ref,s,mi (1/days) of behavioral models
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Table 4 Initial parameter ranges and posterior parameter statistics of solute concentration factor (fc) for plant uptake of behavioral models
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Results of Freundlich n values are shown in Additional file 1: Table S16. Values in the complete initial range (0.7–1.3) in case of PFPeA and 6:2 diPAP, values between 1 and 1.3 in case of PFHxA, values at the upper boundary in case of PFHpA and PFOA and values at the lower range (8:2 diPAP) were found. Reasons for a wide range could be a not given sensitivity or equifinality, since higher KD and lower n might result in the same value of sorption strength, especially if the information content of the measured values is not enough to parameterize a non-linear isotherm or if the isotherm is in fact linear.

Anion exclusion posterior parameter statistics (Additional file 1: Table S17) show a complete use of the range for PFPeA and PFHxA and values at the boundary of initial values for PFHpA and PFOA. The small initial range of anion exclusion for the PFAA was the result of an internal model error when a bigger range was used as in [41]. An increase of the upper boundary of anion exclusion was rejected due to sufficient model results and only their maximum being on the boundary.

Results of degradation rate of diPAP \(\mu\) ref,l,mi and NER rate \(\mu\) ref,s,mi, only regarding PFOA, are given in Table 3. NER rate of PFOA had a similar magnitude to the given optimized range of PFOA from other modeling studies: 1.5–4.4 10–3/days [41], 3.0–6.6 10–3 1/days [38] with the range being overall lower, which might be the result of small differences in the soil composition.

Degradation rates of diPAPs are in a wide range, with the maximum value of 8:2 diPAP being lower than the maximum value of 6:2 diPAP and the minimum value being the opposite. This might be the result of interaction with other parameters, such as KD-value compensating for changes in the value of the degradation rate, ending up in equifinality. The ranges of degradation rate of 6:2 diPAP are similar (0.45 1/days, strategy II) to another modeling study [41], but one order of magnitude higher than in a laboratory study [19], where transformation rates were calculated with a first-order degradation (0.048 1/days). Degradation rate of 8:2 diPAP is one order of magnitude higher compared with another modeling study (0.05 1/days, strategy II) [41] and two orders of magnitudes higher than in a laboratory study [19], in which the rate had a value of 0.006 1/days. A possible reason for differences is the uncertainty of transformation dynamics between start and end of study, which was estimated through leaching dynamics of transformation products in this study and in another simulation study [41], and was measured in the laboratory study [19] with more data points for calculations. Furthermore, the rates calculated in this study were affected by soil moisture and temperature (Eq. 1). Thus, the actually used transformation rates during the modeling process were presumably lower most of the time, when optimum degradation conditions were not present. Additionally, in soils with saturated zones, the soil moisture factor in the degradation rate calculations of MACRO might not be suitable, because the degradation can decrease at high soil moisture due to low oxygen level [60], as discussed in [41].

The calibrated factor fc is dependent on the chain length of PFAS (see Table 4), which can be attributed to the decreasing water solubility with increasing chain length [61]. Previously calibrated uptake factors for PFOA [38], showed values one to three orders of magnitude lower than the values obtained here. Other reasons for differences between the various uptake factors for PFOA are (1) different uptake factors for different plant species [62]; (2) different values for substance parameters, which also influence the uptake factor; and (3) a lower contamination situation here compared to Gassmann et al. 2021 [38], with uptake masses of > 0.1 mg per year.

Some of the substance parameters are correlated with each other, which means that other parameter combinations can also lead to similarly good results, since certain effects can be represented by different parameter values. A mutual influence was observed, for example, between the KD value and the degradation rate (r8:2 diPAP = 0.85, p < 0.001), the KD value and NER formation (rPFOA = − 0.55, p < 0.01), the KD value and Freundlich n (rPFHpA = 0.56, p < 0.001 und rPFHxA = 0.55, p < 0.001), KD value and fc for 6:2 diPAP and the upper soil (r8:2 diPAP = 0.85, p < 0.001), Freundlich n value and fc for 6:2 diPAP (r6:2 diPAP = − 0.72, p < 0.001) and KD value and \(\mu\) ref,l,mi for both diPAP (r6:2 diPAP = 0.91, p < 0.001 and r8:2 diPAP = 0.96, p < 0.001) with high significance levels determined through the Pearson rank correlation test (Additional file 1: Table S18 and S19). The connection lies in the sorption equilibrium for the mentioned parameters. The lower the KD value, the more is present in the liquid phase, and vice versa. To achieve a similar effect, a decrease in the KD value should be accompanied by a reduction in the degradation rate in the liquid phase or an increase in NER formation in the solid phase. The significant correlations were not equally observed for all substances in the mentioned combinations.

Implications for contamination cases

When considering Fig. 5, the relationship between simulated temperatures and soil moisture content becomes evident, showing an inverse correlation (r = − 0.73, p < 0.001), which can be attributed to evapotranspiration.

Fig. 5
figure 5

Simulated minimum and maximum soil temperatures (°C) in the upper 30 cm (a). Simulated soil water content of the whole lysimeter (L/m2) (b) of an example simulation

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For the model, this modified approach suggests that high temperatures (spring/summer) and high moisture content, but still unsaturated (fall/winter), favor the degradation process. Therefore, degradation would occur throughout the year, except during temperatures below 0 °C, as degradation is not considered at these temperatures in the MACRO model if the temperature-dependent degradation is enabled. For real cases of diPAP contamination, a worst-case scenario for leaching of transformation products towards groundwater would occur during a mild summer with precipitation or precipitation after a warm but not dry period and in soils with a high water permeability, such as the sandy soils. This favors leaching of transformation products, such as at the beginning of fall until spring. Figure 5 also shows that the optimum conditions for transformation are hardly reached at all.

Another study [39], which simulated PFOA with and without precursor transformation in the saturated zone could be connected to a model such as presented here, to predict the leaching in the unsaturated soil for real contamination scenarios.

Conclusions

The use of models to represent the behavior of PFAS in the environment is crucial given the recorded cases of contamination. Results show that the transformation, leaching of diPAPs and their transformation products, soil retention, and plant uptake can be represented with the chosen model setup in MACRO. The influence of temperature and soil moisture on the transformation of diPAP worked to represent observed values, but the calculation of the transformation rate based on temperature and soil moisture was directly adopted from the model and should be investigated separately to verify this approach and potentially make adjustments if necessary.