Soil CO₂ uptake involves not only fluxes of CO₂ over the soil surface but also beneath the soil. To compute CO₂ fluxes over the soil surface, a PVC column is set to measure CO₂ concentration above the soil in a closed chamber. As shown in Eqs 1, 2 in Wang et al. (2016c), the net soil CO₂ release (F_c) can be computed by F c = d C ( t ) d t = k ( t ) ρ V p v c S p v c ∗ ∆ C O 2 ∆ t = k ( t ) ρ r h r + 2 h ∗ ∆ C O 2 ∆ t (1) where r, h, V_pvc, and S_pvc are the height, radius volume, and surface area of the PVC column, respectively; ρ is the CO₂ density under the standard state; and k is a dynamic transform coefficient.

A temperature-dependent Q₁₀ model has been widely utilized, in which Q₁₀ is the derivative of the exponential chemical reaction-temperature equation originally developed by Van’t Hoff (1898). With T_as defined as the air temperature at 10 cm above the soil surface, θ_s the soil volumetric water content at 0–5 cm, and R₁₀ the referred F_c at 10°C, then Q₁₀ is the factor by which F_c is multiplied when T increases by 10°C. According to Eqs 1–3 described by Wang et al. (2015b), the part of F_c unexplained by the Q₁₀ model is attributed to the inorganic component of F_c. Alternatively, the soil CO₂ uptake (F_x) can be computed by F o = R 10 Q 10 ( T a s − 10 ) / 10 (2) F i = F c − F o (3) F i + = ( F i + | F i | ) / 2 , F i − = ( F i − | F i | ) / 2 (4) F x = F i − (5) F x = f ( p H ) + g ( T a s , θ s ) (6) where F_o and F_i are the organic and inorganic components of F_c, respectively.

Equation 6 can be further reconciled as F x = F x n p ( E V n p ) + F x l p ( E V l p ) (7) where F_xnp and F_xlp are the linear and nonlinear components of F_x, respectively. EV_np and EV_lp are the sets of environmental variables for the linear and nonlinear components, respectively.

As seen in Chen et al. (2014), the main drivers for F_x are pH, T_as, θ_s; thus, F x n p ( E V n p ) = f ( p H ) = r 7 q 7 p H − 7 ,   F x l p ( E V l p ) = g ( T , θ s ) = λ T + μ θ s + e (8) where the pH belongs to EV_np and T_as and θ_s belong to EV_lp.

For computation, the empirical coefficients from Chen et al. (2014) and Wang et al. (2015b) can be directly used. That is, F x n p ( E V n p ) = 3.0191 × 0.7625 p H − 7 (9) F x l p ( E V l p ) F x l p ( E V l p ) = 0.0059 T a s + 0.0003 θ s − 2.5081 (10) where F_x is hypothetically attributed as pH-driven, T_as-driven, and θ_s-driven CO₂ uptake by soils.

Two adaptive methods—partial least-squares regression (PLSR) and a machine learning model (ANN)—were used to examine the environmental contributors of pH, T_as, and θ_s. Backpropagation was utilized in the machine learning processes with ANN. The performance statistics of the ANN calibration were explicitly displayed and the environmental contributors with relatively small contributions (<5%) were excluded from the ANN model performance. The PLSR model was performed on a random partition of the dataset (70% for training, 30% for testing) and ANN models were assessed against the whole data set. The major steps of the PLSR calibration are shown in Figure 1 (Zhou et al., 2021).

Six calibration processes were performed during PLSR. The first was the standardization, which was done before Step 1. The second process was to find the correlation coefficient matrix, where X and Y were put into an augmented matrix that was included in Steps 2 and 3. The third process was to find the pair of principal components. This process was included in Step 4, where the Lagrange multiplier method was utilized. The fourth subsequent process involved the calculation of the contribution rate table, in which the contributions of each environmental contributor were determined individually. The fifth process was to select k principal component pairs according to the contribution rate table, which was used in the sixth and seventh processes to carry out the final regressions between environmental contributors and the main drivers for soil CO₂ uptake. The eighth process performed cross-validation with the above PLSR components.

However, PLSR also has some limits. PLSR is a linear model, which is advantageous for determining the contributions of individual environmental variables. However, the best model might be nonlinear. Meanwhile, ANN cross-validation is also required to ensure that the selected determining factors from PLSR remain dominant in nonlinear models. The ANN aims to imitate the working mechanisms of the human brain. Neurons are connected to form each layer of the neural network. Each layer transmits information through a function operation running on the connection between each layer. By adjusting the connected weights between each layer, the neural network can output the desired target. This goal needs to be achieved through the training of the neural network, which is within the allowable range of error. The basic information transfer function for the connection between each connection layer is xw + b, where x is the information passed from the previous layer, w is the weight reflecting the relevance, and b is the deviation. As the brain sometimes needs to choose to transmit or ignore received information, neural networks filter information through an activation function. The major steps in ANN for updating parameters are shown in Figure 2 (Zhou et al., 2021; Zhuang et al., 2021).

Environmental data-driven PLSR-ANNs were collected from a series of previous studies (Chen et al., 2014; Zhou et al., 2021; Zhuang et al., 2021). The present study further hypothesized that the precipitation amounts (P_a) and groundwater level (GL) were another two elements in EV_np. Based on the results of PLSR and machine learning, the other environmental variables; namely, air humidity (AH), air pressure (AP), soil temperature (T_s), soil salinity (SS), and wind speed (WS) and direction (WD) were included in EV_lp. Evidence for the above two hypotheses is presented in Sections 3 and 4. The calibration errors were quantified using R ² and RMSE, as described by Farifteh et al. (2007) and Zhou et al. (2021).

According to Eq. 10, soil CO₂ uptake can be reinforced by reducing T_as. The reinforcement degree is −0.0059 μmol m⁻² s⁻¹ when T_as decreases by 1°C. We hypothesized that T_as was a function of other environmental variables; that is, T a s = T a s f ( A H , A P , T s , S S , W S , W D , p H , G L , θ s , P a ) (11)

The hypothetical mechanisms in the function T_f are as follows. T_s can affect T_as because T_s is a direct reflection of the surface heat condition. Since the volume heat capacity of water is much larger than that of air, AH, GL, WD, WS, P_a, and θ_s can affect T_as. Decreases in AP indicate that the air above the soil is expanding and T_as is increasing. Since soil water and salt transport can be aggravated by higher T_as, SS and pH are also potential indicators for local T_as. Under these hypotheses, the reinforcement of T_as-driven CO₂ uptake is possible if one of the environmental variables AH, AP, T_s, SS, WS, WD, pH, GL, θ_s, and P_a can be changed through human activities.

The results of the PLSR-ANN analyses present some basic evidence for Eq. 11. As shown in Figure 3, the PLSR results demonstrated the very accurate prediction of T_as by a linear combination of other environmental variables (R²=0.894 and RMSE=2.975 on the training data set, R²=0.939 and RMSE=2.507 on the testing data set). These results were further demonstrated by the ANN (R²=0.924 and RMSE=2.495 before excluding the secondary contributors, R²=0.887 and RMSE=2.966 after excluding the secondary contributors).

From the PLSR results, the function T_asf can be approximated by T a s = c 0 + c 1 A H + c 2 A P + c 3 T s + c 4 S S + c 5 W S + c 6 W D + c 7 p H + c 8 G L + c 9 θ s + c 10 P a (12) where the contributions of AH, AP, T_s, SS, WS, WD, pH, GL, θ_s, and P_a to T_as can be calculated from the coefficients c₁, c₂, …, c₁₀, in which c₀ is the residual.

The computed coefficients for Eq. 12 were c₁=−2.0413, c₂=−1.4424, c₃=2.3231, c₄=−1.3964, c₅=0.3635, c₆=−0.1313, c₇=1.6382, c₈=−1.9786, c₉=0.6742, c₁₀=0. Hence, the leading environmental contributors to T_as were T_s, AH, GL, pH, AP, SS and θ_s, with contributions to T_as of 19.4%, 17%, 16.5%, 13.7%, 12%, 11.6%, and 5.6%, respectively. Among these leading environmental contributors, GL was significantly affected by human activities and can also influence pH, SS, and θ_s. Therefore, we can try to reinforce T_as-driven soil CO₂ uptake in arid regions through groundwater management, which is associated not only with irrigation decisions but also with living plans and industrial water use. A decrease in GL by 1 m means a T_as reduction of 1.9786°C and a reinforcement of F_x by −0.0117 μmol m⁻² s⁻¹ according to Eqs 10, 12.

According to Eq.10, soil CO₂ uptake can be reinforced by reducing θ_s. The reinforcement degree is −0.0003 μmol m⁻² s⁻¹ when θ_s decreases by 1%. We hypothesized that θ_s was a function of other environmental variables; that is, θ s = θ s f ( A H , A P , T s , S S , W S , W D , p H , G L , T a s , P a ) (13)

The hypothetical mechanisms in the function θ_sf are as follows. Precipitation and evaporation are the two most important factors influencing θ_s. Therefore, P_a affects θ_s. Since T_s and T_as can directly reflect the surface heat conditions, the θ_s values under different temperatures can vary. Except for precipitation and evaporation, atmospheric environments, soil properties, and surface vegetation also affect θ_s. Hence, AP, AH, WD, WS, SS, and pH can potentially affect θ_s. The influence of GL on θ_s is easily understood. In arid regions, soil water is mainly supplied by groundwater. A decrease in GL can directly induce the decrease of θ_s. Under these hypotheses, θ_s-driven CO₂ uptake can be reinforced if one of these environmental variables can be changed through human activities.

The results of the PLSR-ANN analyses present some basic evidence for Eq. 13. As shown in Figure 4, the PLSR results suggest that the best linear combination of other environmental variables can only explain about half of the variations in θ_s (R²=0.552 and RMSE=0.577 on the training data set, R²=0.51 and RMSE=0.663 on the testing data set). However, we cannot conclude that the function θ_sf in Eq. 13 does not exist. The ANN results suggest that θ_s can be correctly predicted by a nonlinear combination of the considered environmental variables (R²=0.9 and RMSE=0.274 before excluding the secondary contributors, R²=0.904 and RMSE=0.283 after excluding the secondary contributors).

From the PLSR results, the function θ_sf cannot be approximated by θ s = c 0 + c 1 A H + c 2 A P + c 3 T s + c 4 S S + c 5 W S + c 6 W D + c 7 p H + c 8 G L + c 9 T a s + c 10 P a (14) where the computed coefficients from PLSR are c₁=−0.1691, c₂=−0.0238, c₃=0.2133, c₄=0.3858, c₅=0.0326, c₆=−0.102, c₇=−0.0202, c₈=−0.219, c₉=0.1813, c₁₀=0.

These computed coefficients further reveal that the PLSR results are not convincing. Thus, the leading contributors are SS, GL, T_s, T_as, AH, and WD, with contributions to θ_s of 28.6%, 16.3%, 15.8%, 13.5%, 12.6%, and 7.6%, respectively. While the results are wrong to exclude P_a, we can obtain significant information from the two subfigures in Figures 4C,D. No significant differences in ANN performance were observed before and after excluding the secondary contributors. They were both very robust. Since Eq. 14 excluded WS, AP, pH, and P_a as the second contributors to θ_s, there must be another important contributor among T_s, T_as, GL, WD, SS, and AH.

Although the ANN results present a very accurate prediction of θ_s by a nonlinear combination of the considered environmental variables, we cannot determine the best θ_sf from ANN. Consequently, we are motivated to choose the most important contributor to θ_s among T_s, T_as, GL, WD, SS, and AH. Since GL can be influenced by human activities and the management of groundwater sources has attracted attention (Daliakopoulos et al., 2005; Wang et al., 2016d; Cruz-Paredes et al., 2021), we prefer to choose GL. As shown in Figure 5, θ_s fluctuates when GL varies from 65 to 90 m in irrigation seasons.

GL is also a well-known factor associated with θ_s (Buttle, 1989). Irrigation decisions can significantly affect θ_s and other soil properties (Rawls et al., 1982). In Section 3.1, GL is a suitable controller to reinforce T_as-driven soil CO₂ uptake. Benefitting from a suitable plan on water use for living and industry, we can effectively control GL that can, in turn, affect θ_s. In particular, we can try to reinforce θ_s-driven soil CO₂ uptake in arid regions through proper irrigation decisions and groundwater use plans. Considering Figure 5 as an example, it is easy to see that the relationships between GL and θ_s are complicated. When GL increased from 68 to 78 m, θ_s decreased from 15.88% to 13.70%. Thus, an increase in GL at this stage led to a 2.18% decrease in θ_s, which reinforced F_x by −0.001 μmol m⁻² s⁻¹ according to Eqs 10, 13.

According to Eq. 9, soil CO₂ uptake can be reinforced by increasing soil pH. Both T_as and θ_s belong to EV_lp, while pH belongs to EV_np. Since F_x(EV_np) is an exponential function, the reinforcement degree of F_x can differ when the pH is increased from different starting points. For example, F_x can be reinforced by −0.7170 μmol m⁻² s⁻¹ with a pH increase from 7 to 8. However, when the pH is increased from 8 to 9, the F_x is reinforced by only −0.5467 μmol m⁻² s⁻¹.

We can hypothesize that pH is a function of other environmental variables; that is p H = p H f ( A H , A P , T s , S S , W S , W D , θ s , G L , T a s , P a ) (15)

However, as we learned in Section 3.2, the PLSR-ANN results cannot help us directly identify the leading contributor unless the hypothesized function can be approximated by a linear function. Thus, pH_f may be approximated by a linear function. As proper irrigation decisions and groundwater source management have been recommended to reinforce both T_as-driven and θ_s-driven CO₂ uptake, we directly hypothesize that pH is a nonlinear function of GL; that is p H = p H f ( G L ) (16)

The hypothetical mechanisms in the function pH_f are as follows. Fluctuation of GL significantly affects soil salt transport, which in turn changes the salt composition of the soil. Since soil pH is majorly influenced by salt composition, pH can be approximated by a nonlinear function of GL. Eq. 16 is proved to be robust (R²=0.978, RMSE=0.028), as shown in Figure 6. Hence, the hypotheses with Eq. 16 are not only reasonable but are also robust in predicting soil pH.

Under these hypotheses, pH-driven CO₂ uptake can be reinforced through human activities. Similar to the strategies in Sections 3.1 and 3.2, only a suitable plan on water use for living and industry is required to ensure that the GL fluctuations are advantageous for reinforcing soil CO₂ uptake. Considering Figure 6 as an example, it is easy to see that the relationships between GL and pH are also complicated. When GL increased from 65 to 70 m, the pH increased from 9.40 to 10.03. Therefore, a GL increase at this stage caused a pH increase of 0.63, leading to a −0.2473 μmol m⁻² s⁻¹ reinforcement of F_x according to Eqs 10, 16. However, when GL increased from 70 to 90 m, the pH increased from 10.03 to 9.40. Therefore, a GL increase at this stage caused a decrease in pH of 0.63, which cannot reinforce F_x.