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Study areaFigure 2 shows the location of the study area on a map of China generated by ArcGIS software. This study’s field experiments were carried out in the Shuanghe Town agricultural comprehensive water-saving demonstration area (40°42′ N; 107°24′ E), which is located in the middle reaches of the Hetao Irrigation Area of Inner Mongolia. The duration of the experimental process ranged from April in 2018 to October in 2020. The experimental area was characterized by a mid-temperate semi-arid continental climate. The average annual precipitation was determined to be 138 mm and the average evaporation was approximately 2332 mm. The majority of the rainfall was concentrated during summer and autumn seasons, and the accumulation of salt in the surface soil was considered to be serious in the spring and winter months. The average rainfall during maize growth period was 75.3 mm. The 0 to 40 cm soil layers in the experimental area were categorized as silty loam soil, with an average bulk density ranging from 1.42 to 1.53 g cm−3. A maize straw layer with a thickness of 5 cm was buried at a depth of 40 cm, and then the land was leveled. Also, in addition to autumn watering and spring irrigation procedures, water from the Yellow River was used three times for irrigation during the entire growth period of the maize crops. The adopted irrigation method belonged to border irrigation. Urea (46% N) were used as the fertilizer types.Figure 2The location of the study area.Full size imageField trials design and data collectionWe carried out experiment 1 from 2018 to 2019, and the data obtained were used for model training and to determine the hyper-parameters. The experimental design is shown in Table 1. The PNN model trained from the data obtained in experiment 1 predicted the optimal range of irrigation amount and nitrogen application rate (N rate) for each growth period of maize. In these ranges, the soil organic matter and total nitrogen could be kept above 20 g/kg and 1.6 g/kg, respectively, the soil salt content was less than 2 g/kg, and the pH value was between 6.5 and 7.5. In order to verify the accuracy and feasibility of the range of irrigation and nitrogen application simulated by PNN, the field experiment 2 was set in 2020 based on the range simulated by PNN and to evaluate the fitting degree between measured and simulated values of soil indicators under the same amount of irrigation and nitrogen application. The experimental design is shown in Table 2.Table 1 Experimental 1 design scheme.Full size tableTable 2 Experimental 2 design scheme.Full size tableThe experimental design were repeated for three times. The plot area of each treatment measuring 8 × 9 = 72 m2. The surrounding area was separated using 1.2 m buried polyethylene plastic film, and 30 cm was left at the top to prevent fertilizer and water from flowing into each other. The field management process was consistent with that used by the local farmers. The film width of maize was 1.1 m, with each film covering two rows. The plant spacing was approximately 45 cm, and the row spacing was 35 cm. In addition, the planting density of the maize was 60,000 plants/hm2.During the entire growth period of the maize crops, soil samples were collected from the 0 to 20 cm, 20 to 40 cm, 40 to 60 cm, 60 to 80 cm, and 80 to 100 cm soil layers using a soil drill and a three-point method was adopted. The soil samples were stored at 4 °C for the determination of total nitrogen, organic matter, total salt content, and pH values. The total nitrogen, organic matter, total salt content, and pH were determined using a KDN-AA double tube azotometer, MWD-2 microwave universal digestion device, TU1810PC ultraviolet–visible spectrophotometer, and a TU18950 double beam ultraviolet–visible spectrophotometer, respectively.Soil parameters measured include organic matter (SOM), total nitrogen (TN), Salt and pH. The data set includes pre-irrigation and post-irrigation reports from 2018 to 2020. Statistical parameters regarding the soil data are shown in Table 3.Table 3 Various meteorological variables and their descriptive statistics.Full size tableThe dataset obtained in Experiment 1 in 2018 to 2019 was 2490 rows in size, the 80/20 principle was used to data into training, and testing sets were required for ML modeling; 80% of data were employed for model training, while the remaining 20% were used for testing. Specifically, the data corresponding to the treatments with the nitrogen application rate (N rate) of 75 kg/hm2 (N3) in all the treatments (W1N3, W2N3, W3N3) were used as the test set, and the data of the other treatments were used as the training set. The training set was used to initiate ML parameter training. Subsequently, The test set was employed to assess the model. The dataset size in 2020 was 1080 rows, which was used to verify ML modeling.Figure 3 shows the changes of soil indexes over time for each treatment in the field test (take the 0–40 cm soil in the main distribution area of maize roots as an example). There are differences under the influence of different irrigation amounts. When irrigation is 90 mm, soil SOM is 13.25% and 7.00% higher than 60 mm and 120 mm, and soil TN is 4.59% and 6.50% higher than 60 mm and 120 mm, respectively. The soil Salt was 23.30% lower than 60 mm, and the pH was 4.16% and 4.36% lower than that of 60 mm and 120 mm, respectively. It can be seen that irrigation of 90 mm is more favorable for increasing soil SOM and TN contents and reducing soil salinity and alkalinity. Soil SOM and TN contents were the highest at n 75 kg/hm2, which were 4.38% and 8.34% higher than those at N = 93.3 kg/hm2, respectively. Soil Salt was the lowest at N = 60 kg/hm2, which was 3.02% lower than those at N = 75 kg/hm2, with a small gap with other levels. In conclusion, nitrogen application of 75 kg/hm2 was beneficial to increase soil organic matter and nitrogen content, and nitrogen application of 60 kg/hm2 was beneficial to controlling soil salt content.Figure 3Changes in soil organic matter, total nitrogen, salinity, and pH under different treatments over time (a case study of 2019).Full size imageMachine learning (ML) models used for irrigation and nitrogen application strategiesFive ML frames were used to estimate the irrigation and N rate. These models are preference Neural Network (PNN), Support Vector Regression (SVR), Linear Regression (LR), Logistic Regression (LOR), and traditional BP Neural Networks (BPNN). Among them, the prediction effects of linear, Poly, and rbf kernel functions are respectively tried in SVR framework. The torch framework was used to train and test machine learning models in Python.Development of preference neural networkModel frameworkThe preference neural network (PNN) which was proposed for the first time in this study was a typical deep learning model. PNN can be regarded as an approximate natural function in order to describe the complete dependence of the soil fertility indexes, including the effects of soil total nitrogen, organic matter, total salt content, and pH values on irrigation and nitrogen applications. More specifically, PNN has the ability to optimize the function by constructing the mapping y = f (x, θ) and learning parameter θ.First, the input end of PNN model was defined as matrix X ∈ ℝn×d (in which n is the sample size, n = 2490; and d is the dimension of each input vector, d = 6), where {xi} i=1, …, n ∈ X represents the vectorized set of total nitrogen, organic matter, salt content, and pH used for measuring the soil fertility, as well as the nitrogen application and irrigation durations (expressed by days after sowing). At the same time, the output end of the model was defined as the matrix Y ∈ ℝn×2, which represented the levels of the irrigation and nitrogen fertilizer applications. The goal of the proposed PNN model was to learn the fixed mapping Y′ = f (X; θ) ⇒Y through the given input matrix X, where θ is the well optimized learnable parameters which can be obtained via PNN training. Meanwhile, the predicted value Y′ will infinitely approach the measured value Y. The structure and the algorithm of this study’s PNN model is shown in Fig. 4 and Table. 4.Figure 4Schematic diagram for the PNN structural connections. In the figure, it can be seen that when each input vector passed through each layer of the PNN, it is first multiplied by the Hadamard product of the weight matrix and preference value matrix for the purpose of obtaining a weight matrix with preference properties. After the matrix was activated by the Relu Function, Batch Normalization Module Methods and the Dropout Module were used for random suspension and normalization processing, and the input of the next layer was obtained.Full size imageTable 4 Algorithm of Preference neural network.Full size tableLayer-by-layer affine transformationA good definition of the affine transformation of the information flow between layers is considered to be the key to neural network model training. Generally speaking, the learnable parameter θ of each layer of a model includes the weight parameter w and the preference parameter b. The hidden representation hl of the l-th layer in PNN is defined as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{mathrm{T}}{W}_{l}+{b}_{l}$$
(1)

where Wl and bl represent the learnable weight and bias variables of the l layer, respectively, and hl-1 is the hidden representation of the upper layer. Therefore, when l = 1, then h0 = X.In the present study, using the hierarchical update rules, a given input data stream was allowed to pass through each hidden layer with intermediate operations, and then finally reached the output end.Preference structureThe correlation between different production behavior factors (e.g., irrigation levels) and different natural factors (e.g., soil organic matter) differs in agricultural production. However, the traditional fully connected neural network has the characteristic that nodes of one layer are fully connected with all nodes of subsequent layers, resulting in the neurons between production behavior factors and natural factors with very weak correlation still all being connected. Conversely, connections between neurons corresponding to factors with solid correlations are not strengthened.Therefore, in this study the preference value module was specially developed. By first calculating the correlation and significance between different production behavior factors (irrigation amount, N rate) and different soil fertility factors (organic matter, total nitrogen, total salt and pH), the preference value between the above two types of variables was calculated, and the preference matrix was constructed. Then the Hadamard product of the weight matrix and preference matrix was used to realize the artificial intervention and guidance to the neural network’s learning process.In order to reduce the adverse impact of non-normality of data on correlation analysis as much as possible, this study rank-based inverse normal (RIN) transformations (i.e., conversion to rank score) methods were used to normally process the data28. The RIN transformation function used here is as follows:$$f(x)={Phi }^{-1}left(frac{{x}_{r}-frac{1}{2}}{n}right)$$
(2)

where Φ–1 is the inverse normal cumulative distribution function, and n is the sample size.The normal cumulative distribution function is represented as follows: for discrete variables, the sum of probabilities of all values less than or equal to a, and its formula is as shown below:$${F}_{X}(a)=P(Xle a)$$
(3)
The RIN normalized conversion values meet the requirements of normal distribution, Pearson correlation analysis and t-test can be directly performed, and the formula used was as follows:$$r(X,Y)=frac{mathrm{Cov}(X,Y)}{sqrt{left(mathrm{Var}left[Xright]mathrm{Var}left[mathrm{Y}right]right)}}$$
(4)

where r (X, Y) is the Pearson Correlation Coefficient, Var [X] is the variance of X, and Var [Y] is the variance of Y, Cov (X, Y) is the covariance of X and Y, which represents the overall error of the two variables. The t-test is performed on the normalized data after rank-based inverse normal (RIN) transformation method, and the formula is as follows:$$t=sqrt{frac{n-2}{1-{r}^{2}}}$$
(5)

where n is the number of samples, and r represents the Pearson Correlation Coefficient. Preference value is the concentrated embodiment of correlation and significance between variables, and the calculation formula is as follows:$${PV}_{ij}=frac{r({X}_{i},{Y}_{j})}{{P}_{ij}+e}$$
(6)

where PVij represents the preference values between the variables Xi and Yj, Xi represents the ith production behavior factor (e.g., irrigation amount), and Yj represents the jth soil fertility factor (e.g., soil organic matter content), ({P}_{ij}) is obtained by looking up the table based on the t, and e is a constant, taking 0.001 in order to prevent the denominator of the formula from being 0.In order to make the preference values of the various indicators in the same order of magnitude more stable, the preference values were normalized:$${PV}_{normal}=pm frac{left|{PV}_{i}-{PV}_{avg}right|}{sqrt{frac{sum_{i=1}^{N}{({PV}_{i}-{PV}_{avg})}^{2}}{N-1}}}$$
(7)

where N represents the number of variables related to the experimental treatments, PVi -PVavg takes the absolute value, while the positive or negative values of the PVnormal were determined by the positive or negative values of the correlation r.The PNN integrated the preference matrixes into the neural network structures by identifying the Hadamard products of the learnable weights between the preference matrixes and the input and output data. By referring to Eq. (1) in the hierarchical affine transformation, the preference constraint of PNN could be expressed as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{T}{W}_{l}odot P+{b}_{l}$$
(8)

where P is the preference matrix calculated by Eq. (8), and ⊙ represents the Hadamard product of the corresponding elements of the matrix. The structure of preference neural network and preference value are shown in Figs. 5 and 6.Figure 5Schematic diagram of the preference connection structures of the preference neural networks. The depth of the network detailed in the figure only illustrates the preference connection structure (for a better demonstration), and does not indicate the depth of the PNN used in the experiment.Full size imageFigure 6PVnormal between production behavior factors and natural factors. Since soil depth, days, irrigation amount and N rate were all artificially set variables, and there was no objective correlation in the data set. Therefore, the preference values among these variables were default e = 0.001.Full size imageHyper-parameters of PNNWe conducted experiments on the datasets with varying the hyper-parameters (such as the number of PNN layers and hidden layers, the number of nodes in each layer, learning rate, dropout rate and batch size) to understand that how the Hyper-parameters impact on the performance of PNN.We select the activation function and learning rate by referring to the neural network structure commonly used in similar fields (1 hidden layer and 64 hidden nodes)29,30. It is found that ReLU has better performance than other activation functions (sigmoid, tanh). The performance is best when the learning rate is around 0.005. It is generally believed that neural networks with more hidden layers are able, with the same number of resources, to address more complex problems31, but excessively increasing network depth will easily lead to overfitting32. Since there is no direct method to select the optimal number of hidden layers and nodes33, this study first calculated the structure of one hidden layer and 64 nodes in each layer, and found that the combined effect was poor (R2 of irrigation and nitrogen application were 0.3971 and 0.4124, respectively). Therefore, the trial-and-error method is adopted. The number of hidden layers starts from 1 and is incremented by 1 to test the maximum number of 10 hidden layers. The number of nodes in each layer were tested with a maximum number of 100 hidden neurons, starting with 5 and increasing by 5.We found that when the number of hidden layers of PNN exceeds 6, and the number of nodes in each layer exceeds 65, the performance will drop significantly. The reason behind this phenomenon could be the current dataset size is insufficient for larger scale of the PNN model. In the consideration of that the size of new dataset we can obtain very year is similar to the current dataset size, we believe that current hyper-paramter settings of PNN is in a reasonable condition.After that, the number of layers was fixed as 6, and the number of nodes in each layer were tested 10 times with 60 as the starting point and 1 as the increment, we found that when the number of nodes was 64, the improvement of the fit degree was no longer noticeable. On this basis, we changed different activation functions and learning rate again, and found that PNN still has the best performance when the activation function is ReLU and the learning rate is 0.005. Then, different batch sizes and dropout rates were tried. The two parameters had weaker effects on the performance than the other parameters, and the performance was optimal at 256 and 0.1, respectively.The hyper-parameters include:

1.

number of PNN layers;

2.

number of hidden layers;

3.

types of activation function;

4.

percentage of dropout;

5.

learning rate;

6.

loss function;

7.

optimizer;

8.

batch size;

9.

number of epochs;

10.

number of workers.

The ideal PNN structure for the study comprises these layers:

1.

number of PNN layers is 8;

2.

number of hidden layers is 6;

3.

Fully connected layers with 64 nodes and ReLU activation function

4.

dropout with 0.1.

5.

the learning rate is 0.005;

6.

loss function is Huber Loss Methods (HLM);

7.

optimizer: ADAM;

8.

epochs is 500;

9.

the batch size is 256;

10.

number of workers is 6.

Hyper-parameters of other modelsLR algorithms and LOR do not have hyper-parameters that need to be adjusted. A part of the hyper-parameters of the SVR model was determined by referring to Guan Xiaoyan’s research34, and a part of the hyper-parameters of the BPNN model was determined by referring to Gu Jian’s research27. RMLP takes the same hyperparameters as PNN. The hyperparameters of SVR and BPNN models are shown in Table 5.Table 5 Hyper-parameters of other model.Full size tableModel performance evaluationThe proposed PNN model was trained and validated using the field measured data from 2020 and the performance achievements of PNN were evaluated by the root mean square errors, mean square errors, and mean absolute errors as follows:$$RMSE=sqrt{frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{n}}$$
(9)
$${R}^{2}=1-frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{iavg})}^{2}}$$
(10)
$$MAE=frac{{sum }_{i=1}^{n}left|{y}_{ipre}-{y}_{iavg}right|}{n}$$
(11)
Model multidimensional fertility targetsThe soil fertility grade classification of soil organic matter, soil total nitrogen content and salt content in this study was based on the soil fertility grade classification results by the Agriculture and Animal Husbandry Bureau of Bayannur City, along with the local standard Technical Specifications for the Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), as the shown in Tables 6 and 7.Table 6 Soil organic matter and Soil total nitrogen degrees.Full size tableTable 7 Grading of the salinization degrees.Full size tableIn the evaluation system of soil fertility referencing the Technical Specifications for Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), the pH was divided into four grades according to the membership degrees of the land productivity evaluations, as detailed in Table 8.Table 8 pH grading degrees of the cultivated land.Full size tableBased on the classification standard of soil fertility obtained by the Bureau of Agriculture and Animal Husbandry of Bayannur City, when the farmland soil is at the high fertility level, the soil organic matter and total nitrogen content should be more than 20 g/kg and 1.6 g/kg, respectively. Soil salt content was less than 2 g/kg. Meanwhile, the pH value is kept between 6.5 and 7.5. More

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Knowing the distribution of species is crucial for effective conservation action. However, accurate and high-resolution spatial data are only available for a limited number of species1,2. For mammals and birds, the most comprehensive and widely used global distribution dataset is the set of range maps compiled as part of the assessments for the International Union for Conservation of Nature (IUCN) Red List. These represent each species’ distributional limits and tend to minimize omission errors (i.e. false absences) at the expense of commission errors (i.e. false presences)3,4. Therefore, they often contain sizeable areas not regularly occupied by the species.Maps of the Area of Habitat (AOH; previously known as Extent of Suitable Habitat, ESH) complement range maps by indicating potential occupancy within the range, thereby reducing commission errors5. AOH is defined as ‘the habitat available to a species, that is, habitat within its range’5. These models are produced by subtracting areas unsuitable for the species within their range, using information on each species’ associations with habitat and elevation5,6,7,8. Comprehensive sets of AOH maps have been produced in the past for mammals6 and amphibians7, as well as subsets of birds8,9. The percentage of a species’ range covered by the AOH varies depending on the methodology used to associate species to their habitats, and their habitats to land-cover, the coarseness of the range map, the region in which the species is distributed, and the species’ habitat specialization and elevation limits5. For example, Rondinini et al.6 found that, when considering elevation and land cover features for terrestrial mammals, the AOH comprised, on average, 55% of the range. Ficetola et al.7 obtained a similar percentage when analyzing amphibians (55% for forest species, 42% for open habitat species and 61% for habitat generalists). Beresford et al.8 found that AOH covered a mean of 27.6% of the range maps of 157 threatened African bird species. In 2019, Brooks et al.5 proposed a formal definition and standardized methodology to produce AOH, limiting the inputs to habitat preferences, elevation limits, and geographical range.AOH production requires knowledge of which habitat types a species occurs in and their location within the range1. Information on habitat preference is documented for each species assessed in the IUCN Red List10, following the IUCN Habitats Classification Scheme11. However, the IUCN does not define habitat classes in a spatially explicit way, therefore, we used a recently published translation table that associates IUCN Habitat Classification Scheme classes with land cover classes12. Species’ elevation limits were also extracted from the IUCN Red List.We developed AOH maps for 5,481 terrestrial mammal species and 10,651 terrestrial bird species (Fig. 1). For 1,816 bird species defined by BirdLife International as migratory, we developed separate AOH maps, for the resident, breeding, and non-breeding ranges, according to the migratory distribution of the species (Fig. 2). The maps are presented in a regular latitude/longitude grid with an approximate 100 m resolution at the equator. On average, the AOH covers 66 ± 28% of the geographical range for mammals and 64 ± 27% for birds. We used the resulting AOH maps to produce four global species richness layers for: mammals, birds, globally threatened mammals and globally threatened birds13 (Fig. 3).Fig. 1Spatial distribution maps of Tangara abbas. Maps represent (a) the geographic range21, and (b) the Area of Habitat (AOH) of the species. The AOH was produced by subtracting unsuitable habitats from the geographical range. This species’ habitats are forest and terrestrial artificial habitats and has elevation range of 0 – 1600 m.Full size imageFig. 2Spatial distribution maps of Cardellina rubrifrons, divided into resident, breeding and non-breeding areas for this migratory species. Maps represent (a) the geographic range21, and (b) the Area of Habitat (AOH) of the species. The AOH was produced by subtracting unsuitable habitats from the ranges. This species is a forest species with elevation rangelimits of 1500 – 3100 m.Full size imageFig. 3Global species richness maps for (a) terrestrial mammals (considering 5,481species) and (b) terrestrial birds (considering 10,651 species). Calculated by overlaying all species’ AOH per class, resulting inon the number of species at each grid cell, latitude/longitude grid at a resolution of 1°/1008 or approximately 100 m at the equator (EPSG:4326) with the ellipsoid WGS 1984.Full size imageThe AOH maps presented in this paper are more useful for some purposes than global species distribution models, as they reduce and standardize commissions14. They are especially useful for not well-known and wide-range species. However, we note that for well-known species alternative sources may have more accurate distributions15. Moreover, AOHs are affected by the bias and errors of the underlying data, especially relevant errors associated with documentation of species’ habitats and elevations, and the translation of habitats into land cover classes, given that habitat is a complex multidimensional concept that is challenging to match to land-cover classes12, and that the current version of the IUCN Habitat Classification Scheme on IUCN’s website is described as a draft version11.The AOH maps have multiple conservation applications5,16,17, such as assessing species’ distributions and extinction risk, improving the accuracy of conservation planning, monitoring habitat loss and fragmentation, and guiding conservation actions. AOH has been proposed as an additional spatial metric to be documented in the Red List5, and is used for the identification of Key Biodiversity Areas18. More

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Surface morphology analysisSEM images were shown in Fig. 1. It showed that the contour of three soils were fairly clear before adsorption. But it became fuzzier and the degree of cementation was increased when phenanthrene was adsorbed on the soils. According to the surface morphology, the silty sand (A) had furrows on the surface before adsorption compared with the fairly smooth without any furrows after adsorption (B). The silts (C) were flaky and the lamellar accumulation decreased (D). The loess (E) had a smooth surface with some flaky and rod like structure, after adsorption (F), the surface of loess increased in clay-like structure.Figure 1SEM micrographs of the three soil samples. (A) Silty sand; (B) Adsorbing 5 h of Silty sand; (C) Silts; (D) Adsorbing 5 h of Silts; (E) Loess; (F) Adsorbing 5 h of Loess.Full size imageAdsorption and desorption experimentsAdsorption and desorption kineticsAdsorption kinetics is one of the most important characteristics governing solute uptake rate and represents adsorption efficiency33. The sorption and desorption kinetics of phenanthrene in three soils were shown in Fig. 2. The results showed that the adsorption processes among all soils were similar. The kinetics of phenanthrene in soils was completed in two steps: a “fast” adsorption and a “slow” adsorption. The adsorption amount increased during 0-18h. It was a rapid reaction from 0 to 200 minutes. From 200 to 600 minutes, the adsorption amount increased slightly into balance. This phenomenon was due to the adsorption of phenanthrene occurred on the surface of soil organic matter. With the increase of time, soil surface adsorption sites were gradually saturated, causing the decrease of adsorption rate until reaching the equilibrium. Phenanthrene was a hydrophobic substance. It was easy to reach the soil surface and adhere to the grain surface. The results were consistent with the study of had also found that the balance time was approximately 18h and the adsorption amount increased with the adsorption reaction time34. Under the same conditions, loess had the highest adsorption capacity, which was mainly due to the highest organic content 18. The maximum phenanthrene sorption capacities ranked as follows: loess > silty sand > silts. As shown in Fig. 2, phenanthrene desorption in soils was relatively quick and its desorption equilibrium time was 3h. To reach an adequate desorption balance while remaining consistent with the adsorption reaction time, the balance time of the adsorption–desorption experiment was set at 18h. Generally, PAHs below 4 cycles could reach the adsorption equilibrium for about 16~24h.Figure 2(a)Adsorption equilibration curves of phenanthrene sorption in soils. (b) Desorption equilibration curves of phenanthrene sorption in soils.Full size imagePseudo-second-order and Elovich models were used to study the phenanthrene adsorption mechanism (Table 3). Phenanthrene sorption kinetics were satisfactorily described by a pseudo-second-order model with coefficients of determination (R2) ranging from 0.99875 to 0.99847, compared with R2 values of 0.26508–0.73901 for the Elovich model. This well-fitting pseudo-second-order model indicated that the rate-limiting step was chemical adsorption, including electronic forces through sharing or exchange of electrons35,36. Moreover, it suggested that sorption was governed by the availability of sorption sites on the soil surfaces instead of by the phenanthrene concentration in solution.Table 3 Constants and coeffients of determination of Pseudo-second-order kinetics and Elovich models of sorption.Full size tableAdsorption and desorption isothermsThe isotherm was used for quantitative analysis of phenanthrene transport from liquid to solid phase and for understanding the nature of interactions between phenanthrene and the soil matrix. The sorption and desorption isotherms of phenanthrene in soils were shown in Fig. 3. The data showed that phenanthrene adsorption and desorption capacities of three soils varied markedly due to their different physicochemical properties. With the increase of phenanthrene concentration, the adsorbed amount increased. At the same temperature, the adsorption capacity of silty sand was minimum while loess was maximum. This is mainly related to the soil physicochemical properties. At the same initial concentration, the temperature increase from 20 °C to 40 °C showed that the adsorption and desorption capacity decreased with temperature increase. On the one hand, the rise of temperature can increase the phenanthrene solubility in the liquid phase. On the other hand, it could reduce various forces between the soil surface and phenanthrene37.Figure 3(a)20 °C adsorption isotherms for phenanthrene in soils. (b)30 °C adsorption isotherms for phenanthrene in soils. (c)40 °C adsorption isotherms for phenanthrene in soils. (d) 20 °C desorption isotherms for phenanthrene in soils. (e) 30 °C desorption isotherms for phenanthrene in soils. (f) 40 °C desorption isotherms for phenanthrene in soils.Full size imageThe Freundlich isotherm was used mainly for adsorption surfaces with nonuniform energy distribution, and the Langmuir isotherm was used for monolayer adsorption on perfectly smooth and homogeneous surfaces38. The experimental data were fitted with the Langmuir and Freundlich adsorption models, and the isotherm parameters logKF, 1/n, KL, qmax and the coefficient of determination (R2) of phenanthrene in soils were listed in Table 4.Table 4 Isotherm parameters for Phenanthrene sorption in soils.Full size tableAs shown in Table 4, according to the coefficients of determination (R2), all soils were better fitted with the Freundlich model, which assumes that phenanthrene sorption and desorption occurs on a heterogeneous surface with the possibility of sorption being multi-layered39. This phenomenon has also been observed in humic acid and nanometer clay mineral40. It showed that the soil adsorption of organic matter was not only surface adsorption but also the process of soil organic matter distribution41,42,43 reached the equilibrium isotherm fitted well with the Freundlich equation when studying the adsorption behavior of aromatic compounds by solids.Adsorption and desorption thermodynamicsTo clarify the adsorption mechanisms, the thermodynamic parameters mentioned earlier were calculated and presented in Table 5. Generally, the value of Gibbs free energy changeΔG0 indicated the spontaneity of a chemical reaction. Therefore, it could evaluate whether sorption was relate to spontaneous interaction44. Negative values of ΔG0 indicated that the feasibility and spontaneous nature. The research was under the temperature range about 293–313 K. For adsorption process, all soils ΔG0 was  0 and desorption ΔH  1, P  temperature  > phenanthrene concentration  > pH. In the interaction, the phenanthrene concentration and organic matter have a significant effect on the silt adsorption rate. The coefficient of determination of the silt complex correlation is R2 = 0.9464, indicating that the response model has a good fit, and the experimental error is within the acceptable range. Adjusting the complex correlation coefficient R2 = 0.8982 indicates that the regression relationship can explain 89.82% of the change in the dependent variable. Therefore, this The model can be used to analyze and predict the effect of different factors on the adsorption rate of phenanthrene.3D response surface analysisIn response surface optimization, the three-dimensional response surface graph reflects the influence of the interaction of the other two variables on the response value, and the slope of the response surface reflects the significance of the interaction of the two variables on the response value. The more significant the interaction effect is on the response value, when the slope is gentle, the effect is not significant. If the contour map is elliptical, it indicates that the interaction between the two variables is significant, and if the contour map is circular, it is not significant46. In addition, the slope and density of the contour line also reflect the influence of the variable on the response value. The steeper the contour line and the greater the density, the greater the influence of the variable on the response value47.

(1) Loess Fig. 5 is a three-dimensional response surface diagram of the interaction between initial phenanthrene concentration and pH to phenanthrene adsorption on loess. It can be seen from the figure that the slope of the response surface graph is steep, and the contour line is an approximate circle, indicating that the interaction between phenanthrene concentration and pH is not significant for the response value. With the increase of pH, the adsorption rate of phenanthrene on loess showed a slow decline at first to the lowest point at 6, and then gradually increased. When the soil pH was close to 6, with the increase of the initial phenanthrene concentration, the adsorption rate of loess also showed a trend of first decreasing and then increasing. According to the F value, F = 0.337, P = 0.5532  > 0.05, it can be concluded that soil pH and initial phenanthrene concentration of the solution have no significant interaction on the adsorption rate of loess.

Figure 6 shows the effects of initial phenanthrene concentration and organic matter on phenanthrene adsorption on Loess under the condition that pH value and temperature are at the central point. It can be seen from the figure that the initial phenanthrene concentration and soil organic matter contour are steep, indicating that their interaction is significant. The range of phenanthrene adsorption rate is 70 ~ 95, and the change of surface is steep. From the Loess error analysis, it can be seen that if f value is 6.05 and P value is 0.0275  More

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