Three Bayesian tracer models: Which is better for determining sources of root water uptake based on stable isotopes under various soil water conditions?

doi:10.21203/rs.3.rs-1527587/v1

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Three Bayesian tracer models: Which is better for determining sources of root water uptake based on stable isotopes under various soil water conditions?

https://doi.org/10.21203/rs.3.rs-1527587/v1

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Background and aims Stable isotope methods provide a powerful technique to quantify the sources of plant root water uptake (RWU). Although many models coupled with stable isotopes have been developed to estimate RWU, little is known about their pros and cons, especially their performance under different soil water content (SWC) conditions.

Methods In this study, three Bayesian mixing models, including MixSIAR, MixSIR and SIAR, were tested their merit and demerit in determining RWU of winter wheat with six sampling events under various SWC conditions (normal, dry and wet) in the North China Plain.

Results The proportions of RWU in different soil layers showed significant differences among the three Bayesian models, for example, the proportion of 0-20 cm soil layer calculated by MixSIR, MixSIAR and SIAR were 69.7%, 50.1% and 48.3% for the 3rd sampling under the dry condition, respectively. Furthermore, the average proportion of 0-20 cm layer under dry condition was lower than that under normal and wet conditions, taken MixSIR as an example, being 51.4%, 82.5% and 65.4%, respectively. The performance of three models in determining plant water source appointment varied with SWC conditions: the performance indicators such as coefficient of determination, Nash-Sutcliffe efficiency coefficient in MixSIAR were higher than that in MixSIR and SIAR, showing that MixSIAR performed well under the normal and wet condition. While the rank of performance under the dry condition was MixSIR, MixSIAR and SIAR, respectively.

Conclusions Overall, MixSIAR performed relatively better than other models in predicting RWU under various soil moisture conditions.

stable isotopes

root water uptake

water source apportionment

soil water content

Bayesian model

Root water uptake (RWU) plays a key role in the process of soil-plant-atmosphere continuum (SPAC) water cycling (Chang et al., 2019; Grossiord et al., 2017; Vargas et al., 2017). The principal sources of plant RWU include precipitation, irrigation, groundwater, and soil moisture. Root system mostly determine the RWU source, and their development was significantly affected by soil moisture (Jasechko et al., 2013; Sprenger et al., 2016; Zhao et al., 2018). Studying these questions: which main water sources do root absorb, what proportion of each source contributes to the plant, and how does the RWU pattern change along with soil water conditions, are of substantial importance for providing reasonable irrigation and fertilization management in agriculture (Liu et al., 2021; Ma and Song, 2016; Zhao et al., 2018). However, traditional methods, such as root extraction and plant physiology measurement, are much difficult to precisely quantify the proportion in RWU (Asbjornsen et al., 2007; Liu et al., 2018; Stock and Semmens, 2016). Also, several mathematical models in combination with the Richards equation (e.g., Feddes) can provide a detailed description of RWU pattern based on principles of soil hydraulic dynamics. However, these models are prone to measurement errors due to the heterogenous distribution of soil hydraulic properties, variations of roots growth, and the difficulty of long-term monitoring of these parameters (Li and Yue, 2018; Schwartz et al., 2016; Zhang et al., 2020a).

Stable isotopes (δD and δ¹⁸O) analysis for estimating RWU has gained great attention in forest, grass, and farmland ecosystems (Chang et al., 2019; Hoekstra et al., 2014; Yang et al., 2018), as the high sensitivity and accuracy in determining the proportional contribution of water sources. Previous studies have confirmed that no isotope fractionation occurred during water transfer from the soil to the roots through xylem vessels (Coelho and Or, 1999). Thus, the δD and δ¹⁸O in plant xylem water can be regarded as a mixture of potential water sources in different proportions (Grossiord et al., 2017; Mora and Jahren, 2003; Zhao et al., 2016). According to isotopic mass balance, the fundamental isotope mixing formulation using δD and δ¹⁸O to determine the contributions (f_i) of three sources (i = 1, 2, 3) to plant (p) is as follows:

$${{\delta }\text{D}}_{\text{p}}={\text{f}}_{1}{{\delta }\text{D}}_{1}+{\text{f}}_{2}{{\delta }\text{D}}_{2}+{\text{f}}_{3}{{\delta }\text{D}}_{3}$$

$${{{\delta }}^{18}\text{O}}_{\text{p}}={\text{f}}_{1}{{{\delta }}^{18}\text{O}}_{1}+{\text{f}}_{2}{{{\delta }}^{18}\text{O}}_{2}+{\text{f}}_{3}{{{\delta }}^{18}\text{O}}_{3}$$

$$1={\text{f}}_{1}+{\text{f}}_{2}+{\text{f}}_{3}$$

Here, the contributions of three sources to plant can be calculated with two isotope signatures. If the number of sources exceeds three sources, then the model is mathematically underdetermined, with no unique solution (Phillips et al., 2005).

However, some algorithms can be used to quantify water source partitioning with more unknowns than equations. For example, the multi-source mass balance model (IsoSource) and Bayesian mixing models have been applied to determine the proportion of water contribution from each source (Phillips et al., 2005; Rossatto et al., 2012; Stock et al., 2014). Even though IsoSource made up the complicated problem when the number of sources exceeds the number of tracers, this model neither could provide an exact proportion of RWU nor incorporate the uncertainty of δD and δ¹⁸O in the water source (Parnell et al., 2010; Phillips et al., 2005). However, Bayesian tracer mixing models, including MixSIAR, MixSIR, SIAR, have been proven to obtain more reliable results of RWU due to it comprises prior information and accounts for the variability in tracer data (Moore and Semmens, 2008; Parnell et al., 2013; Stock et al., 2018). Nevertheless, inconsistent or contradictory results would output caused by different model structures or algorithms, which make these results are incomparable among studies (Jackson et al., 2008; Parnell et al., 2013; Rothfuss and Javaux, 2017; Stock et al., 2014).

In addition, the performance of different mixing models in RWU source appointment have been further explored in several studies (Evaristo et al., 2017; Rothfuss and Javaux, 2017; Wang et al., 2019; Zhang et al., 2020b). Wang et al. (2019) compared three models and suggested that SIAR and MixSIAR performed much better than the MixSIR using field data of three plant species in the semiarid Loess Plateau of China. However, Zhang et al. (2020) reported that the MixSIR model presented better performance in RWU than the SIAR model. Nevertheless, previous studies mainly focused on comparing model performance with filed data, which may neglect the impact of soil moisture on model performance. For example, Zhang et al. (2020) indicated that RWU proportion varied along with the plants growing seasons among mixing models: there were significant differences in the dry seasons, whereas no difference was found in the wet seasons. Thus, it is necessary to investigate whether the wet or dry growing conditions affect the performance of the models in predicting the water source partitioning.

To remedy this deficiency, three Bayesian tracer mixing models, including MixSIAR, MixSIR and SIAR, were selected to determine the proportion of RWU in different soil layers and evaluate their performance. The soil and xylem isotope (δD and δ¹⁸O) data of winter wheat under different soil water content (SWC) conditions (normal, dry and wet) were collected to determine the RWU proportion in the North China Plain. There were two specific objectives. First, to compare the difference in the proportional contributions of each soil layer among three Bayesian models; Second, to evaluate the performance of three mixing models under different SWC conditions.

Study site

Field sample collections were performed in Dianzi (118.29 °E, 37.06 °N, 13 m Altitude), Boxing County of Shandong Province, China. The region is characterized by a temperate continental monsoon climate. The annual mean rainfall and air temperature were 601 mm and 12.5 ℃, respectively. The precipitation during winter wheat growth season only accounts for 20–30% of the annual precipitation, which is far less than the demand of wheat grows (Si et al., 2020). The mean rainfall during 2017–2020 winter wheat seasons were 253.5, 95.5 and 162.7 mm, respectively. The mean air temperature during 2017–2020 winter wheat seasons were 8.2, 8.4 and 8.8℃, respectively. The basic information of soil properties are showed in Table 1. The mean soil available nitrogen (N), phosphorous (P), potassium (K) and soil organic carbon (SOC) were 59.69, 10.67, 127.57 mg kg^− 1, and 1.33%, respectively.

Table 1

Basic information of soil properties in 0-100 cm layer
Soil depth (cm)	Clay (%)	Silt (%)	Sand (%)	Field capacity (g g^− 1)	Saturated water content (g g^− 1)	Bulk density (g cm^− 3)
0–20	5.25	78.55	16.20	0.25	0.32	1.41
20–40	6.33	77.74	15.94	0.21	0.26	1.52
40–60	7.63	76.89	15.48	0.21	0.24	1.54
60–80	8.23	76.92	14.85	0.21	0.25	1.53
80–100	8.79	78.90	12.31	0.21	0.24	1.52

The winter wheat variety in 2017–2018 season was Jimai-22, and the variety of Jimai-23 was used in 2018–2020 seasons due to variety alternative. The wheat was sown in early October and harvested in next early June. Irrigation of 90 mm was applied on April 2, 2018, and on March 28 and May 10, 2019, and on March 20 and May 7, 2020 in the three wheat seasons, respectively. Samples were collected in three plots (9 m × 20 m). The base fertilizer rates of N: P₂O₅: K₂O were 120-120-120 kg ha^− 1, and the topdressing N fertilizer 120 kg ha^− 1 was applied at early jointing stage.

Sample collection and isotopic analyses

Wheat stem and soil samples were collected for stable isotopes measurement at the different growth stages (jointing, heading, flowering, filling, and harvest). In addition, at 3 days after both irrigation and rainfall and before irrigation, the xylem and soil samples were collected with three replicas. The wheat xylems between the soil surface and the first node about 2–3 cm in length were collected. Around the sampled wheat plants, soil cores from 0 to 150 cm depth (at 0 ~ 5, 5 ~ 10, 10 ~ 20, 20 ~ 30, 30 ~ 40, 40 ~ 60, 60 ~ 80, 80 ~ 100, 100 ~ 120 and 120 ~ 150 cm) were extracted using a soil auger in the three plots. All soil and stem samples were sealed with parafilm and kept stored at -15 ℃ before isotopic measurements. Precipitation or irrigation water were collected at 4 ℃ in each rainfall or irrigation event using a 50 ml polyethylene bottle and sealed with parafilm.

Soil water content (SWC, cm³ cm^− 3) was measured by the Insentek sensors (Beijing Oriental Ecological Technology Ltd., Co., Beijing, China) at 10 cm increment in 0–60 cm depth, 20 cm increment in 60–120 cm depth and 30 cm increment in 120–150 cm depth. Accuracy and reliability of the sensors for measuring SWC were assessed in the previous study (Qin et al., 2021). Further, we also use the oven-dry method to correct the SWC measured by sensors. Based on the soil water balance, the daily crop evapotranspiration (ET_total, mm) and the daily changes in soil water storge of each soil layer (ET_each, mm) can be obtained using Insentek sensors.

A cryogenic vacuum distillation system (LI-2000, LICA United Technology Limited, Beijing, China) was used to extract water from stem and soil samples. To avoid evaporation fractionation, all water samples were stored in a refrigerator at 4 ℃ before isotopic analysis. The isotopic measurements for D and ¹⁸O content were conducted using a Continuous-Flow Isotope-Ratio Mass Spectrometer (Delta V Advantage, Thermo Fisher Scientific, Bremen, Germany). All water samples were calibrated against the Vienna Standard Mean Ocean Water standard (V-SMOW) and then convert to δD and δ¹⁸O, expressed as ${\delta }\left(\text{‰}\right)=\frac{{\text{R}}_{\text{s}\text{a}\text{m}\text{p}\text{l}\text{e}}-{\text{R}}_{\text{s}\text{tan}\text{d}\text{a}\text{r}\text{d}}}{{\text{R}}_{\text{s}\text{tan}\text{d}\text{a}\text{r}\text{d}}}\times 1000=\left(\frac{{\text{R}}_{\text{s}\text{a}\text{m}\text{p}\text{l}\text{e}}}{{\text{R}}_{\text{s}\text{tan}\text{d}\text{a}\text{r}\text{d}}}-1\right)\times 1000$.

Model description

Three Bayesian mixing models, including MixSIAR, MixSIR and SIAR, were used to determine plant RWU proportion. There is no isotope fractionation occurred during water transfer from the soil to the roots and through xylem vessels, thus the fractionation values were set to 0 in the Bayesian models (Donovan and Ehleringer, 1994). The average and standard deviation value of the stem and each source isotopic compositions (δD and δ¹⁸O) were input into the three Bayesian models. Meanwhile, these Bayesian models output a source water’s most likely contribution to the stem water (Evaristo et al., 2017; Stock et al., 2018; Wang et al., 2019). For SIAR, the model was run with 500,000 iterations (discarding the first 50,000) using Markov chain Monte Carlo (MCMC) built on R software. The MixSIR used sampling importance resampling (SIR) algorithm, and the model was run with 500,000 iterations. The run length of the MCMC was set to ‘long’ and the error option was set to ‘residual only’ in MixSIAR. The more detailed information of three models can be referred to literatures (Moore and Semmens, 2008; Parnell et al., 2013; Stock et al., 2018; Wang et al., 2019).

Data preparation and model performance assessment

In this study, three different soil moisture conditions, i.e. normal, dry and wet condition, were used to evaluate the performance of different models.

Normal condition: the soil moisture ranged between 70% and 90% of field capacity without soil water movement by gravity in the 0–100 cm soil column (i.e. one week after irrigation).

Dry condition: the soil moisture ranged between 40% and 60% of field capacity due to the consumption of crop development.

Wet condition: the soil moisture ranged between 80% and 100% of field capacity and the gravity water flows within the 0–100 cm soil column after irrigation (within a week after irrigation).

Although we can currently analyze the process of water absorption by roots through models and experiments, it is still difficult to obtain the true value of the proportion of water contributed from each source to plant. Therefore, we indirectly evaluate the accuracy of different models by evaluating the matching degree between observed and predicted values of isotopic compositions of stem water. Based on the theory that the stem isotopic compositions (δD and δ¹⁸O) can be considered as the mixture of different water sources and thus the calculation of predicted value (P_i) was expressed as follows:

$${\text{P}}_{\text{i}}=\sum _{\text{i}=1}^{\text{n}}{\text{f}}_{\text{i}}{{\delta }}_{\text{i}}$$

where ${\text{f}}_{\text{i}}$ represents the proportion of water contributed from each source i (n = 4 in this study), and ${{\delta }}_{\text{i}}$ indicates the measured isotopic composition of the corresponding water source i.

Model performance indicators such as the coefficient of determination (R²), the root mean square error (RMSE), the index of agreement (IA), the Nash-Sutcliffe efficiency coefficient (NS) were adopted to evaluate the model prediction accuracy by comparing the matching degree between observed and predicted values of stem water isotopic compositions.

The equations used for RMSE was:

$$\text{R}\text{M}\text{S}\text{E}=\sqrt{\frac{1}{\text{n}}\sum _{\text{i}=1}^{\text{n}}{\left({\text{P}}_{\text{i}}-{\text{O}}_{\text{i}}\right)}^{2}}$$

where n is the number of validation samples. Regarding the value of RMSE, lower values implied the less error and accuracy of the models.

The equations used for R² was:

$${\text{R}}^{2}={\frac{\sum _{\text{i}=1}^{\text{n}}({\text{P}}_{\text{i}}-{\text{P}}_{\text{a}\text{v}\text{e}})({\text{O}}_{\text{i}}-{\text{O}}_{\text{a}\text{v}\text{e}})}{\sqrt{{\sum }_{\text{i}=1}^{\text{n}}{({\text{P}}_{\text{i}}-{\text{P}}_{\text{a}\text{v}\text{e}})}^{2}}\sqrt{{\sum }_{\text{i}=1}^{\text{n}}{({\text{O}}_{\text{i}}-{\text{O}}_{\text{a}\text{v}\text{e}})}^{2}}}}^{2}$$

where the P_ave and O_ave are the mean of the predicted and observed values, respectively. The closer the R² to 1, the more perfect agreement between P_i and O_i value.

The equations used for IA and NS was:

$$\text{I}\text{A}=1-\frac{\sum _{\text{i}=1}^{\text{n}}|{\text{P}}_{\text{i}}-{\text{O}}_{\text{i}}|}{\sum _{\text{i}=1}^{\text{n}}{\left(\right|{\text{O}}_{\text{i}}-\text{O}}_{\text{a}\text{v}\text{e}}|+\left|{\text{P}}_{\text{i}}-{\text{O}}_{\text{a}\text{v}\text{e}}\right|)}$$

The value of IA, based on a calculation of dispersion, ranged from 0 to 1. An IA value of 1 meant more awesome prediction in the models. An IA value close to 0 indicated a worst agreement between P_i and O_i value.

The equations used for NS was:

$$\text{N}\text{S}=1-\sum _{\text{i}=1}^{\text{n}}{({\text{P}}_{\text{i}}-{\text{O}}_{\text{i}})}^{2}/\sum _{\text{i}=1}^{\text{n}}{({\text{O}}_{\text{i}}-{\text{O}}_{\text{a}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}})}^{2}$$

The value of NS also measured the effectiveness of the model. It was reported the simulation results were regarded as perfect prediction in water-limited ecosystems if the NS value is close to 1 and as less reliable if the NS value is negative (Wang et al., 2019). In addition, we used field data from our previous study at the same site to verify which model predicts best for water source apportionment.

Statistical analysis

According to the similarities of SWC, soil layer classifications was analyzed using a hierarchical cluster analysis (HCA) method described in Zhao et al., 2018. The statistical analysis was performed in SPSS 25.0 (SPSS Inc., Chicago, IL, USA). One-way analysis of variance (ANOVA) was used to compare the differences in RWU source partitioning by the different models at α = 0.05. All figures were drawn using Origin 2016 (Origin Lab, Northampton, MA, USA).

Soil water content and isotopic composition of water sources

Soil layer classification based on SWC with the hierarchical cluster analysis method is shown in Fig. 1, the four parts were classified as follows: 1) 0 ~ 20 cm; 2) 20 ~ 60 cm; 3) 60 ~ 100 cm; 4) 100 ~ 150 cm. SWC measured at different sampling times under different soil moisture conditions is shown in Fig. 2. SWC was significantly different under the three SWC conditions, the average SWC was 0.18 under the normal condition, 0.13 under the dry condition and 0.20 under the wet condition, respectively.

The δD and δ¹⁸O of precipitation showed a large fluctuation from − 55.81 to 6.91‰ and − 8.74 to -0.10‰, with mean value of -25.07‰ and − 4.21‰ (Fig. 3). The local meteoric water line (LMWL), which was established based on precipitation data (δD = 6.77δ¹⁸O+3.43, R² = 0.79, P < 0.01), had a lower slope and intercept than that of the global meteoric water line (GMWL) (Craig, 1961). The δD and δ¹⁸O of soil water showed a broad range from − 87.10 to -19.66‰ and − 11.29 to -2.61‰, with mean value of -59.63‰ and − 7.60‰ (Fig. 3). The δD and δ¹⁸O of the 0–20 cm soil layer showed greater variability than those of other soil layers. The slope and intercept values of the soil water line (SWL: δD = 6.25δ¹⁸O- 12.12, R² = 0.88, P < 0.01) were less than those of the LMWL, which indicated that strong evaporative enrichment occurred in soil water.

Determination of the water sources with different mixing models

For the normal condition, MixSIR estimated a higher value of proportional contribution in the in 0–20 cm depth, in comparison to MixSIAR and SIAR (P < 0.05) except at the 2nd sampling time. Nevertheless, the proportions in the other soil layers were similar among the three models, except at the 1st and 5th sampling periods. The specific mean proportion of RWU in different sampling times determined by MixSIAR were 43.3 ± 14.1%, 21.6 ± 6.5%, 18.6 ± 5.2% and 16.5 ± 6.9% in the 0–20 cm, 20–60 cm, 60–100 cm, and 100–150 cm soil layers; 65.4 ± 20.2%, 14.1 ± 13.5%, 12.9 ± 10.2% and 7.7 ± 3.9% in the MixSIR, and 50.5 ± 13.5%, 20.1 ± 6.5%, 16.2 ± 5.4% and 13.2 ± 5.4% in the SIAR model, respectively. As a result, the three Bayesian mixing models indicated that 0–20 cm soil layer was the main RWU depth. Overall, the results suggested that there were significant differences in the proportional contributions of each soil layer in most sampling periods among three Bayesian models (P < 0.05), while no significant difference was found in the main RWU depth among the mixing models under the normal condition.

According to Fig. 4, under the wet condition, the proportion of 0–20 cm layer estimated by the MixSIR was higher in comparison to MixSIAR and SIAR (P < 0.05), such as being 91.4%, 47.1% and 28.8% for the first sampling time, respectively. However, it was lower in other soil depths. The three models showed that 0–20 cm soil layer was the main RWU depth in most sampling times. Nevertheless, the maximum contributions at 5th sampling time derived from 0–20 cm, 20–60 cm and 20–60 cm depth, being that 63.3% for MixSIR, 43.2% for MixSIAR, and 46.2% for SIAR, respectively. In addition, the mean relative contributions of six sampling times were 60.1 ± 14.2%,18.1 ± 13.5%, 11.3 ± 4.7% and 10.5 ± 3.9% in the 0–20 cm, 20–60 cm, 60–100 cm, and 100–150 cm soil layers in the MixSIAR; 82.5 ± 16.1%, 10.3 ± 12.4%, 3.8 ± 2.9% and 3.2 ± 3.1% in the MixSIR and 54.3 ± 15.9%, 21.2 ± 12.6%, 12.6 ± 7.6% and 11.9 ± 9.8% in the SIAR model, respectively.

For the dry condition, there were significant differences in the proportion from shallow (0–20 cm) and middle soil layer (20–60 cm) among the Bayesian models (P < 0.05) except for individual sampling periods (Fig. 4). The mean relative contributions in different sampling times were 39.2 ± 14.1%, 25.9 ± 5.4%, 18.4 ± 5.2% and 16.4 ± 4.4% in the 0–20 cm, 20–60 cm, 60–100 cm, and 100–150 cm soil layers in the MixSIAR; 51.4 ± 24.6%, 20.4 ± 25.9%, 11.6 ± 7.1% and 16.6 ± 13.1% in the MixSIR and 46.4 ± 14.9%, 25.0 ± 7.0%, 15.3 ± 4.7% and 13.2 ± 5.3% in the SIAR model, respectively. Collectively, these results suggested that the average proportion of 0–20 cm layer under the dry condition was lower than that under the normal and wet conditions, indicating that wheat would decrease the RWU proportion of 0–20 cm soil layer under the dry condition due to the less available soil water in shallow layer.

Performance of the Bayesian mixing models in determining water source proportion

Performance of the three mixing models in predicting water source proportion is shown in Fig. 5. For the normal condition, the values of R², RMSE, IA and NS in different sampling times were 0.94, 0.27, 0.87 and 0.93 in the MixSIAR; 0.93, 0.67, 0.68 and 0.58 in the MixSIR; and 0.88, 0.47, 0.83 and 0.80 in the SIAR model, respectively. These results suggested that under the normal condition, the MixSIAR model performed well than the other two models. Under the dry condition, the MixSIR model had a larger value of R², IA, and NS and smaller value of RMSE than the SIAR and MixSIAR model, indicating that MixSIR was more reliable. Interestingly, the accuracy of three mixing models decreased under the wet condition than under the normal and dry condition, but the R² of MixSIAR (0.93) was still higher than other models (Fig. 5). In total, MixSIAR model had a larger value of R², IA, and NS and smaller value of RMSE than the MixSIR and SIAR, suggesting that MixSIAR exhibited relatively better water source apportionment performances in spite of the soil water condition.

Evaluation of water sources apportionment within three Bayesian models

Revealing RWU mechanisms (e.g., how roots grow and how they regulate hydraulic network in response to environmental changes) is critical for modulating plant roots to facilitate water and nutrient uptake. Although new advances have been made on measurement technologies (e.g., root architecture measurements) and mathematical models (e.g., Feddes) over the past decade, in situ measurement of RWU still is difficult to obtain (Li and Yue, 2018; Schwartz et al., 2016; Zhang et al., 2020a). Whereas, in comparison to above methods, the stable hydrogen and oxygen isotopes have been considered an effective tool understanding the temporal and spatial patterns of RWU and, thus, to tackle water management-related questions. Meanwhile, several mathematical models coupled with stable isotopes have been developed to estimate RWU (Phillips et al., 2005; Rossatto et al., 2012; Stock et al., 2014). Among them, these three models (i.e. MixSIAR, MixSIR and SIAR) are most widely used. In theory, the proportion of RWU calculated by the three models is similar because these models are based on the isotopic mass balance. However, different model algorithm or structural was used by model developer to estimate plant water source apportionment due to the problem of more unknowns than equations (Moore and Semmens, 2008; Parnell et al., 2013; Stock et al., 2018). Nevertheless, previous studies mainly focused on selecting one of the models to calculate RWU proportion, which may neglect the differences among the methods for determining plant water source apportionment. So, did model algorithms cause the difference in determining proportional contribution among three mixing models? What about the soil moisture difference?

A recent study suggested that the RWU proportions in shallow layer estimated by the MixSIR model significantly differed from those in the MixSIAR and SIAR, but there was no significant difference between SIAR and MixSIAR (Wang et al., 2019). In this study, the average proportion of 0–20 cm layer estimated by the three models appeared in the order of MixSIR > SIAR > MixSIAR under the normal and dry conditions, while the order was MixSIR > MixSIAR > SIAR under the wet condition. From the perspective of all sampling periods, there was no significant difference (P > 0.05) in the average proportions in the four layers estimated by the three Bayesian models. Nevertheless, from the perspective of individual sampling time, there were significant differences in RWU proportions among the three mixing models (P < 0.05), except for the 2nd and 6th sampling under the normal condition and the 2nd sampling under the wet condition. Interestingly, although there were significant differences in the estimated proportional contributions of each soil layer among the three mixing models, the main RWU depth determined by the three Bayesian models showed no significant differences, except for the 2nd sampling under the dry condition and the 5th sampling under the wet condition. Our results showed that the different models lead to inconsistent RWU proportion under the different SWC conditions. There are probably two comprehensive reasons that contributed to such difference: Firstly, the algorithms difference of the Bayesian models might cause the prediction difference among three models; Secondly, the environment in which crops are grown, especially soil moisture, may also affect the model's prediction results (Stock et al., 2018; Wang et al., 2019). Therefore, it is very important that evaluating the performance of models and choosing a suitable model for determining the RWU proportion.

Several studies reported that the MixSIAR and SIAR model exhibited similar performance and their performance was higher than that of MixSIR (Mabit et al., 2018; Wang et al., 2019), while others indicated that the accuracy of MixSIR was better than that of SIAR (Brett, 2014) or MixSIAR (Zhang et al., 2020b) when without considering SWC conditions. In this study, our results showed that, under the normal condition, the MixSIAR had a smaller RMSE and larger NS-value than MixSIR and SIAR (Fig. 5), suggesting that MixSIAR had more reliable predictions. Compared with the normal condition, the precision of MixSIAR and SIAR was reduced whereas the precision of MixSIR was improved under the drought condition. In particular, the NS-value of SIAR under the dry condition was negative (-0.43), indicating that the effectiveness of model performance was less reliable under the dry condition. After applying irrigation water of 90 mm, the difference between δD and δ¹⁸O of soil water in each layer reduced because water input eliminated the isotopic gradient distribution in the soil profile, which made the model more difficult to determining crop water source partitioning. This may account for the reduced accuracy of these Bayesian models under the wet condition. Collectively, these results suggested that the performance of three models in determining plant water source appointment varied with SWC conditions. Totally, the MixSIAR model showed better performance than the MixSIR and SIAR regardless of the SWC (Fig. 5).

Further, to confirm the above conclusion, we added two group data to check the performance among three models for determining plant water source appointment. One of group additional data from previous study at the same site was used to demonstrate whether the MixSIAR model is better in water source division (Liu et al., 2021). Here, two soil water conditions, i.e., normal and wet condition were considered, due to the fact that the sampling times were less under the drought condition, and the results showed that the input of irrigation water (wet condition) markedly decreased the accuracy of these mixing models. Figure 6a-f presents similar results, the rank of the performance among three models was MixSIAR, MixSIR and SIAR, respectively. Further, another group of data that the relationship between ET_each/ ET_total and proportion of RWU was also used to verify the foregoing conclusion. In fact, the proportional contributions of each soil layer are equal to the ratio of ET_each/ ET_total. Because of the fact that soil evaporation accounts for a small proportion of evapotranspiration, especially in the middle and late period of crop growth (Gao et al., 2014). Thus, the ratio of ET_each/ ET_total, to a large extent, can represent the proportional contributions of each soil layer. As shown in Fig. 6g-i, the results of proportion of uptake calculated by the MixSIAR were much closer to ET_each/ ET_total, indicating that MixSIAR performed better than MixSIR and SIAR.

Implications for water source partitions

Our results, as well as a previous study (Wang et al., 2019), recommended the MixSIAR model as optimal for determining water sources apportionment, owing to its better performance than MixSIR and SIAR. In addition, MixSIAR combined with the advantages of these two models (Stock et al., 2018). Furthermore, we also focused much on the effects of soil water conditions on the model performance. Nevertheless, the simulation of MixSIAR in wet condition were slightly poor, which might be attributed to the stable isotope overlap between potential water sources caused by water migration in soil layer (Meng et al., 2021). Hence, some prior information, for example, the relationships between root traits, soil moisture and nutrient availability, should be implemented to improve the model performance in RWU especially under wet condition (Corneo et al., 2018; Moore and Semmens, 2008; Stock et al., 2018; Wang et al., 2019).

The analysis using stable hydrogen and oxygen isotope provides important evidences for determining the RWU proportion of each sources understanding the seasonal patterns of crop RWU in the agricultural water management. However, the focus on water transport from soil to plant might be too coarse, since soil water movement should pass through the cycle of the soil-plant-atmosphere continuum (SPAC). Therefore, detailed investigations are required to fill essential gaps in water cycle system by combination of other techniques and methods. For example, fertilization application has great effects on water distribution in the soil and plant uptake especially for water-fertilizer integration management (Yan et al., 2021). Thus, more attention should be paid to the effects of relationships between water and fertilizer uptake and their combination efficiency on RWU by using carbon and nitrogen isotopes (El-Sharkawy and Tafur, 2007; Quan et al., 2020; Rocha et al., 2019). In addition, the outputs of RWU only presented a quantitative ratio of crop water use from each soil layer, but the specific amount of root uptake is still unknown. Therefore, it is meaning that combination of stable isotopic method and crop water requirement (ET) to convert the obtained percentages to mm values according to the growth stage, which is very useful to develop to more efficiently and reasonable schemes for farmers and the water managers, particularly in arid and semi-arid regions (Ma and Song, 2018; Wagle et al., 2020; Yang et al., 2018). In the meanwhile, the technique of laser isotope spectrometry provide continuous monitoring of water vapor isotopes with high resolution in the field for further understanding of RWU and evapotranspiration patterns (Aouade et al., 2016; Yuan et al., 2020). Finally, few studies have focused on model analysis of RWU, to deeper understand the mechanism of soil water migration, more studies are needed to integrate with multi-objective isotope models, such as Simple Soil Plant Atmosphere Transfer (SISPAT), to explore the regularity of soil water and stable hydrogen and oxygen isotope transport (Rossatto et al., 2012).

In this study, we evaluated the performance of three mixing tracer models (i.e., MixSIAR, MixSIR, SIAR) for determining RWU under different soil water conditions. The value of water uptake proportions was significantly affected by the three Bayesian models in most sampling periods, such as the proportion of 0–20 cm depth of MixSIR, MixSIAR and SIAR were 50.3%, 31.8% and 43.7% for the 3rd sampling under the normal condition (P < 0.05), respectively. But the main RWU depth estimated by the three Bayesian models showed no significant differences, except for the 2nd sampling under the dry condition and 5th sampling under the wet condition. Generally, the MixSIAR model had a larger value of R², IA, NS and smaller value of RMSE than MixSIR and SIAR models. Thus, according to the characteristics of the model itself and the results of inter-comparison of tracer mixing models combined with the field data, we recommend that the MixSIAR model to estimate plant water source apportionment regardless of the effects of soil water conditions.

Funding: This work was supported by China Agriculture Research System of MOF and MARA (CARS-03-19), the National Natural Science Foundation of China (Grant No. 51879267, 51779259), and the Agricultural Science and Technology Innovation Program (ASTIP), Chinese Academy of Agricultural Sciences.

Conflicts of interest: the authors declare no conflict of interests.

Availability of data: Data available based on reasonable request.

Code availability: Not applicable.

Authors' contributions: Yang Gao and Aiwang Duan planned and designed the experiments. Junming Liu and Zhuanyun Si performed the experiments. Junming Liu analyzed the data and wrote the draft manuscript. Yingying Zhang and Lifeng Wu contributed reagents/materials tools. Yang Gao, Aiwang Duan, Shuang Li and Sunusi Amin Abubakar revised the manuscript. All authors read and approved the final manuscript.

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Three Bayesian tracer models: Which is better for determining sources of root water uptake based on stable isotopes under various soil water conditions?

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