*3.2. Model Comparison for CLQ Evaluation*

In this study, to reduce the calculation burden, variance inflation factor (VIF) was used to perform the analysis of collinearity of the GPPs among four growth stages given a year for developing the models of evaluating CLQ based on 420 sample points. The results in Table 3 indicate that there is collinearity among the GPPs in the four growth stages. Therefore, all data at the four growth stages were selected to construct spectral models.


**Table 3.** The variance inflation factors (VIFs) of MODIS-GPPs at the key growth stages.

In this study, three kinds of models including PLSR, SVR, and GA-BPNN were developed for comparing the evaluation accuracy of CLQ. For each of the years from 2011 to 2015, one PLSR model was obtained based on 294 training samples using CLQ as the response variable and GPPs at the four growth stages as the predictors. With the same training datasets for the years, the corresponding SVR and GA-BPNN models were constructed. The prediction accuracies of CLQ from all the models were assessed based on the values of RMSE, NRMSE and the coefficient of determination (R<sup>2</sup> ) between the estimated and observed CLQ values [45] according to the training and validation samples. The obtained 2011–2015 PLSR evaluation models are:

$$\begin{aligned} \text{C\hat{L}Q} &= 2128.457 + 0.008 \times \text{GPP}\_{\text{Tillering}/2011} + 9.388 \times \text{GPP}\_{\text{joint}/2011} + 14.073 \times \text{GPP}\_{\text{Heading}/2011} \\ \text{GPP}\_{\text{Heading}/2011} &- 4.620 \times \text{GPP}\_{\text{Maturity}/2011} \left( \mathbf{R}^2 = 0.38, \mathbf{P} < 0.001 \right) \end{aligned} \tag{12}$$

$$\begin{aligned} \text{C\%} &Q = 2562.905 + 0.238 \times \text{GPP}\_{\text{Tillering}/2012} + 0.428 \times \text{GPP}\_{\text{Jointing}/2012} + 3.778 \times \text{GPP}\_{\text{Head}/\text{Hy}/2012} \\ \text{GPP}\_{\text{Heading}/2012} &+ 5.437 \times \text{GPP}\_{\text{Maturity}/2012} \left( \text{R}^2 = 0.39, \text{P} < 0.001 \right) \end{aligned} \tag{13}$$

$$\begin{aligned} \text{C\hat{L}Q} &= 2336.989 + 6.886 \times \text{GPP}\_{\text{Tllering}/2013} + 6.834 \times \text{GPP}\_{\text{Jointing}/2013} - 0.401 \times \text{GPP}\_{\text{Heading}/2013} \\ \text{GPP}\_{\text{Heading}/2013} &+ 2.444 \times \text{GPP}\_{\text{Maturity}/2013} \left( \mathbb{R}^2 = 0.40, \mathbb{P} < 0.001 \right) \end{aligned} \tag{14}$$

$$\begin{aligned} \text{C\"L\"Q} &= 2451.9366 + 0.586 \times \text{GPP}\_{\text{Tillering}/2014} + 6.341 \times \text{GPP}\_{\text{Jointing}/2014} + 0.516 \times \text{GPP}\_{\text{Heading}/2014} \\ \text{GPP}\_{\text{Heading}/2014} &+ 6.911 \times \text{GPP}\_{\text{Maturity}/2014} \left( \text{R}^2 = 0.38, \text{P} < 0.001 \right) \end{aligned} \tag{15}$$

$$\begin{aligned} \text{C\"L Q} &= 2328.035 + 3.458 \times \text{GPP}\_{\text{Tillering}/2015} + 3.791 \times \text{GPP}\_{\text{Jointing}/2015} + 5.946 \times \text{GPP}\_{\text{Heading}/2015} \\ \text{GPP}\_{\text{Heading}/2015} &- 4.830 \times \text{GPP}\_{\text{Maturity}/2015} \left( \text{R}^2 = 0.35, \text{P} < 0.001 \right) \end{aligned} \tag{16}$$

For the development of SVR models, the support vector machine (SVM) was selected as epsilon-SVR, its loss function was set as 0.1, and the range of kernel parameter and penalty parameter was set as (2−<sup>8</sup> , 2<sup>8</sup> ) [47]. Moreover, the obtained GA-BPNN models had a three-layer network and a hidden layer with 13 neuron nodes. A total of 1000 iterations was used with 10 maximum runs. Both learning rate and learning objective were 0.01. The mutation probability, crossover probability and population size were respectively 0.1, 0.3, and 10 [36]. The obtained models based on the 294 training samples are compared in Figure 4.

Based on the scattered graphs from the training samples in Figure 4, the points of estimated vs. observed CLQ are overall randomly distributed at both sides of the 1:1 lines. However, the accuracies of the predicted CLQ values vary greatly depending on the models. Overall, the estimates of CLQ from the PLSR models for 2011 to 2015 have smaller R<sup>2</sup> values and greater RMSE and NRMSE values, then the SVR models and the GA-BPNN models. This indicates that the GA-BPNN models performed best, implying that CLQ was nonlinearly correlated with GPPs.

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**Figure 4.** Scatterplots of measured versus estimated CLQ using the training dataset from 2011 to 2015: (**a**–**e**) partial least squares regression (PLSR) model; (**f**–**j**) support vector regression (SVR) model; (**k**– **o**) GA-BPNN model. **Figure 4.** Scatterplots of measured versus estimated CLQ using the training dataset from 2011 to 2015: (**a**–**e**) partial least squares regression (PLSR) model; (**f**–**j**) support vector regression (SVR) model; (**k**–**o**) GA-BPNN model.

In addition, the predicted CLQ values from the models were validated for their accuracy using 126 validation samples in Figure 5. Given a year and a model, the points of predicted vs. measured values of CLQ were randomly placed at both sides of the 1:1 line. But, the PLSR models led to obvious overestimations and overestimations for the smaller and greater CLQ values, respectively. The overestimations were mitigated by SVR models and more mitigation was achieved by the GA-BPNN models. Among the three kinds of models, the GA-BPNN models have the smallest average RMSE In addition, the predicted CLQ values from the models were validated for their accuracy using 126 validation samples in Figure 5. Given a year and a model, the points of predicted vs. measured values of CLQ were randomly placed at both sides of the 1:1 line. But, the PLSR models led to obvious overestimations and overestimations for the smaller and greater CLQ values, respectively. The overestimations were mitigated by SVR models and more mitigation was achieved by the GA-BPNN models. Among the three kinds of models, the GA-BPNN models have the smallest average RMSE of

67.37, than the SVR models with average RMSE of 73.04 and the PLSR models with average RMSE of 92.45 for years from 2011 to 2015, indicating that the GA-BPNN models have the strongest ability of predicting CLQ. of 67.37, than the SVR models with average RMSE of 73.04 and the PLSR models with average RMSE of 92.45 for years from 2011 to 2015, indicating that the GA-BPNN models have the strongest ability of predicting CLQ.

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**Figure 5.** Scatterplots of measured versus estimated values of CLQ using the validation data set of 126 samples from 2011 to 2015: (**a**–**e**) PLSR model; (**f**–**j**) SVR model; (**k**–**o**) GA-BPNN model. **Figure 5.** Scatterplots of measured versus estimated values of CLQ using the validation data set of 126 samples from 2011 to 2015: (**a**–**e**) PLSR model; (**f**–**j**) SVR model; (**k**–**o**) GA-BPNN model.

### *3.3. Mapping CLQ at the Regional Scale 3.3. Mapping CLQ at the Regional Scale*

The rice growth stage GPP-driven spectral model for year 2013 was used to map the CLQ for Aotou Town of the Conghua District and Zhongxin Town of the Zengcheng District to validate its The rice growth stage GPP-driven spectral model for year 2013 was used to map the CLQ for Aotou Town of the Conghua District and Zhongxin Town of the Zengcheng District to validate its

capacity of predicting CLQ at the regional scale in Figure 6. The referenced values of CLQ were grouped into five classes based on the gradation regulations on agriculture land quality in China (*Regulation for gradation on agriculture land quality* GB/T 28407-2012). The R<sup>2</sup> , RMSE, and NRMSE values of the predictions from the GA-BPNN model were calculated based on 60 sample data in Aotou and Zhongxin town, respectively (Figure 7). The prediction accuracies with RMSE of 73.32 and 104.35 and NRMSE of 10.47% and 17.75% show that the GA-BPNN model is appropriate to map CLQ at both towns. capacity of predicting CLQ at the regional scale in Figure 6. The referenced values of CLQ were grouped into five classes based on the gradation regulations on agriculture land quality in China (*Regulation for gradation on agriculture land quality* GB/T 28407-2012). The R2, RMSE, and NRMSE values of the predictions from the GA-BPNN model were calculated based on 60 sample data in Aotou and Zhongxin town, respectively (Figure 7). The prediction accuracies with RMSE of 73.32 and 104.35 and NRMSE of 10.47% and 17.75% show that the GA-BPNN model is appropriate to map CLQ at both towns. capacity of predicting CLQ at the regional scale in Figure 6. The referenced values of CLQ were grouped into five classes based on the gradation regulations on agriculture land quality in China (*Regulation for gradation on agriculture land quality* GB/T 28407-2012). The R2, RMSE, and NRMSE values of the predictions from the GA-BPNN model were calculated based on 60 sample data in Aotou and Zhongxin town, respectively (Figure 7). The prediction accuracies with RMSE of 73.32 and 104.35 and NRMSE of 10.47% and 17.75% show that the GA-BPNN model is appropriate to map CLQ at both towns.

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**Figure 6.** Spatial distributions of the predicted CLQ in 2013 using the GA-BPNN model for the study area: (**a**) Aotou Town and (**b**) Zhongxin Town. **Figure 6.** Spatial distributions of the predicted CLQ in 2013 using the GA-BPNN model for the study area: (**a**) Aotou Town and (**b**) Zhongxin Town. **Figure 6.** Spatial distributions of the predicted CLQ in 2013 using the GA-BPNN model for the study area: (**a**) Aotou Town and (**b**) Zhongxin Town.

**Figure 7.** Measured and estimated CLQ in 2013 using the GA-BPNN model with the 120 validation sample plots for mapping: (**a**) Aotou Town and (**b**) Zhongxin Town. **Figure 7.** Measured and estimated CLQ in 2013 using the GA-BPNN model with the 120 validation sample plots for mapping: (**a**) Aotou Town and (**b**) Zhongxin Town. **Figure 7.** Measured and estimated CLQ in 2013 using the GA-BPNN model with the 120 validation sample plots for mapping: (**a**) Aotou Town and (**b**) Zhongxin Town.

### **4. Discussion 4. Discussion 4. Discussion**

literature in this field.

literature in this field.

The CLQ implies the carrying capacity of land productivity and is critical for food supply and security. However, CLQ often changes dramatically due to human activity induced disturbances and environmental changes [4]. Thus, it is necessary to realize real-time monitoring and evaluation of CLQ in agricultural regions, especially vulnerable or urban fringe areas [48,49]. Previous studies [4,15,16] on remote sensing-based evaluation of CLQ mainly focused on retrieving spectral indicators in both the traditional evaluation system and the PSR framework system. However, it is impossible to acquire accurate CLQ data using the previous evaluation methods due to ignoring spectral relationships of spectral indicators from crop growth stages with CLQ. This study is the first attempt to propose the spectral models relating CLQ to GPP spectral indicators obtained from four growth The CLQ implies the carrying capacity of land productivity and is critical for food supply and security. However, CLQ often changes dramatically due to human activity induced disturbances and environmental changes [4]. Thus, it is necessary to realize real-time monitoring and evaluation of CLQ in agricultural regions, especially vulnerable or urban fringe areas [48,49]. Previous studies [4,15,16] on remote sensing-based evaluation of CLQ mainly focused on retrieving spectral indicators in both the traditional evaluation system and the PSR framework system. However, it is impossible to acquire accurate CLQ data using the previous evaluation methods due to ignoring spectral relationships of spectral indicators from crop growth stages with CLQ. This study is the first attempt The CLQ implies the carrying capacity of land productivity and is critical for food supply and security. However, CLQ often changes dramatically due to human activity induced disturbances andenvironmental changes [4]. Thus, it is necessary to realize real-time monitoring and evaluation of CLQ in agricultural regions, especially vulnerable or urban fringe areas [48,49]. Previous studies [4,15,16]on remote sensing-based evaluation of CLQ mainly focused on retrieving spectral indicators in both the traditional evaluation system and the PSR framework system. However, it is impossible to acquireaccurate CLQ data using the previous evaluation methods due to ignoring spectral relationships of spectral indicators from crop growth stages with CLQ. This study is the first attempt to propose the

stages of late rice phenology for evaluating CLQ. It is expected that this study can enhance the

to propose the spectral models relating CLQ to GPP spectral indicators obtained from four growth

spectral models relating CLQ to GPP spectral indicators obtained from four growth stages of late rice phenology for evaluating CLQ. It is expected that this study can enhance the literature in this field.

Based on the comparison of the evaluation results from three kinds of models, SVR (average R <sup>2</sup> = 0.64 and NRMSE = 9.78%) and GA-BPNN (average R<sup>2</sup> = 0.69 and NRMSE = 8.59%) models performed better than the PLSR model (average R<sup>2</sup> = 0.38 and NRMSE = 11.55%), implying that there is obvious non-linear correlation of CLQ with GPP spectral indicator. This conclusion is consistent with the findings of previous studies [16], indicating that the non-linear models are appropriate. It was also found that the GA-BPNN models provided more accurate predictions of CLQ than the SVR and PLSR models, which was mainly attributed to the integration of BPNN with GA which has the ability of optimizing the BPNN weights and thresholds. For the SVR models, however, the kernel function and penalty factor used only referenced expert experiences and they were limited in the accuracy of CLQ evaluation [50–52].

Based on the field measured GPP values, moreover, the accuracy of the 30 m MODIS GPP generated by the EBK interpolation, with 7.43 of RMSE and 1.59% of RRMSE, was higher than those of the 500 m MODIS GPP, with 33.43 of RMSE and 7.18% of RRMSE, showing the improvements of 26% in RMSE and 5.59% in NRMSE, respectively. These results show that the downscaled 30 m MODIS GPPs were more accurate than the original 500 m spatial resolution products. Although previous studies have shown that machine learning algorithms provide potential on CLQ evaluation, with R<sup>2</sup> of 0.59 and NRMSE of 11.19% [16], the GA-BPNN model proposed in this study shows stronger ability for CLQ evaluation with R<sup>2</sup> = 0.69 and NRMSE = 8.59%, implying that the GPP spectral indicator provides a direct and effective means for estimating CLQ. The further application of the GA-BPNN model to mapping CLQ for Aotou Town and Zhongxin Town resulted in NRMSE values of 10.47% and 17.75% based on 120 validation samples. This indicated that the GA-BPNN model proposed in this study had great potential to map CLQ at a large scale.

It should be noticed that in this study the experiment was conducted only for paddy fields in which cultivated lands often have good and excellent quality. We are currently unable to verify whether the GA-BPNN model based on the relationship of CLQ with GPP can perform well in other types of cultivated lands. Therefore, in the future, we will expand the study to other kinds of cultivated lands with different grades of CLQ. Moreover, in order to further validate the GA-BPNN model for CLQ evaluations, larger sample sizes should be employed. In addition, a limited accuracy assessment using MODIS GPPs with 500 m spatial resolution was undertaken in this study. The spatial resolution of the used images will affect the evaluation accuracy of CLQ because when the rice planted areas that are smaller than the spatial resolution of the images dominate the study area, mixed pixels will exist. The GPP products from finer spatial resolution images acquired from different sensors should be tested. As the correlation coefficient method meets the assumption of normal distribution of data, it was used for determining the use of GPP from the four growth stages. In future study, more powerful methods may be introduced to obtain the growth stages of the crops. Finally, more evaluation algorithms (such as Random Forest and Deep Learning) should be attempted to improve the evaluation efficiency and accuracy for CLQ.

### **5. Conclusions**

This study attempted to obtain an accurate spectral model for evaluation of CLQ based on the GPP spectral indicator at four important growth stages of late rice phenology by comparison of PLSR, SVR, and GA-BPNN models using the measurements of CLQ from 294 training samples and the corresponding GPP data from MOD17 products. This study was conducted in the Zengcheng and Conghua district of Guangzhou City and led to the following conclusions: (1) The downscaled 30 m spatial resolution MODIS GPP data by the EBK interpolation with NRMSE of 1.59% were more reliable than the original 500 m resolution MODIS GPP products with NRMSE of 7.18%; (2) The GA-BPNN spectral model showed the strongest prediction ability for CLQ (RMSE = 60.39) compared to the PLSR and SVM models, indicating the existence of a nonlinear relationship of CLQ with GPP spectral

indicators; (3) The NRMSE values of CLQ predictions from the GA-BPNN model for two validation areas were relatively small (12.14% and 18.39%), further implying that the GA-BPNN model based on rice phenological data could be applied to accurately mapping CLQ at the regional scale. This study is the first report to provide an effective means for CLQ evaluation using a crop growth stage GPP-driven spectral model with GA-BPNN.

**Author Contributions:** M.Z. conceived and designed the experiments; M.Z. and S.L. analyzed the data, created the tables and figures, and finished the first version of the paper; Z.L., Y.H., Z.X., and M.Z. contributed valuable opinions during the manuscript writing; M.Z., Z.X., and G.W. revised the whole manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Natural Science Foundation of China (U1901601); National Key Research and Development Program of China (2018YFD1100103); Guangdong Province Agricultural Science and Technology Innovation and Promotion Project (No. 2019KJ102); and Guangdong Provincial Science and Technology Project of China (2017B030314155).

**Acknowledgments:** We gratefully acknowledge the paper writing assistance of A-Xing Zhu and Yiping Peng, as well as the experimental assistance of Hao Yang and Zhe Ni.

**Conflicts of Interest:** The authors declare no conflict of interest.
