Production Capacity Evaluation of Farmland Using Long Time Series of Remote Sensing Images

Abstract

Farmland is a crucial resource for the survival and evolution of humans. The accurate evaluation of farmland production capacity (FPC) is of great significance for planting structure optimization, the improvement of low-yield farmland and sustainable utilization. The objective of this study is to quantitatively evaluate the FPC at the county scale using time series remote sensing (RS) images. Taking winter wheat as a benchmark crop, the relations between annual yield and the Normalized Difference Vegetation Index (NDVI) were established by a multiple linear regression algorithm. The mean and standard deviations (SD) of the multi-year yield of winter wheat were used to evaluate FPC and its instability using the farmland parcels as the basic unit. The results show that the estimation model for annual winter wheat yield performed best in 2011. The R2 of the modeling sample was 0.93, and the RMSE of the testing sample was 368.1 kg/ha. The FPC grades in the south and north of the study area were relatively high with a good stability, while those in the center were low with poor stability. There was a certain correlation between FPC and soil organic matter (SOM), and the correlation coefficient was 0.525 (p < 0.01). In this study, taking the farmland parcel as a basic unit instead of a pixel, long time series of multi-source RS images with medium resolution were used to monitor the per unit yield of benchmark crops and then evaluate the FPC. This can provide a method for the rapid evaluation of FPC at the county scale.

1. Introduction

Farmland is a crucial resource and environmental factor for human existence and evolution. It has multiple functions that include production and environmental protection, and it is a fundamental guarantee of social stability [1,2]. In recent years, with the rapid development of industrialization and urbanization, both the quantity and quality of farmland in China have been declining, which threatens food security [3]. Ensuring a certain area of farmland and steadily improving its the production capacity is the basis of ensuring food security [4,5]. Therefore, the evaluation of farmland production capacity (FPC) is beneficial to comprehensively grasp the current situation of farmland quality, which is of great significance to the rational use of farmland.

There are many studies on the evaluation of FPC [6,7,8,9]. Some scholars have studied the FPC from the perspective of natural and socio-economic factors affecting the quality of farmland, using statistical methods or combining statistical with GIS spatial analysis [10,11], and then selecting indicators of limiting factors for a comprehensive evaluation of FPC. However, most of the statistical data were obtained by manual surveys, which was at cost of manpower. Most studies on FPC have mainly focused on production potential, which was caused by the impact of crop physiological mechanisms on potential aspects [12]. Currently, the methods of estimating FPC include statistical models [13], remote sensing (RS) models [14], crop growth models, and the combination of crop growth models and RS [15]. In most of these methods, FPC was estimated by monitoring crop yield for one or several years. FPC was not only highly correlated with natural conditions, such as light, temperature, precipitation, and soil [16], but also with human factors such as crop varieties, water and fertilizer management, and farming quality [15,16]. Since the short-term yield information cannot reflect the FPC, it is necessary to use long-term time series yield information for a comprehensive evaluation of FPC.

RS technology can objectively detect the changes in land features, which provided an effective way for monitoring crop growth, grain yield and agricultural disasters [17,18]. Currently, studies on the indicators used to estimate FPC include the enhanced vegetation index (EVI), gross primary productivity (GPP), net primary productivity (NPP), and normalized difference vegetation index (NDVI), which performed well on monitoring crop growth [19,20,21,22,23,24]. Some researchers used the time series EVI of remote sensing images to extract multiple cropping index and active days to evaluate FPC. [19]. Some researchers also used long time series of GPP averages to explore the grades of FPC based on MODIS data [20]. NPP is also used to evaluate the FPC and revealed its spatial differentiation [21]. In addition to those above, NDVI was most widely used in farmland productivity estimation. A large number of studies have shown that NDVI was not only sensitive to changes in vegetation growth, but also could weaken some negative effects caused by solar angle, surface topography, cloud and the change in atmospheric conditions, which was the best indicator of vegetation growth and coverage [22,23,24]. The current application of RS for yield estimation is effective. Low spatial resolution images, such as MODIS, have the advantages of a short revisit period and wide coverage, but the resolution is too low, resulting in mixed pixel phenomenon. It was difficult for the accurate interpretation of multi-crop mixed area, monitoring crop growth and evaluating the FPC. Remote sensing images with a medium resolution, such as Sentinel and Landsat, can be used to grasp the spatial changes of farmland [25]. Therefore, the changes in benchmark crop yield derived from long-time-series RS images with medium resolution can be used to evaluate FPC.

At present, the studies evaluating FPC mainly target a large geographical area with a lack of precise evaluation on the county scale. Additionally, the evaluation of FPC requires monitoring for a long time, and most of the current studies were based on RS images with a low resolution. In this study, we chose to study county-scale areas and used long-time-series multi-source RS images with medium resolution to improve the accuracy of crop identification and per unit yield monitoring and provide a method for regional FPC evaluation.

The purpose of this study is to evaluate the FPC using multi-year yields of benchmark crop derived from remote sensing. It provides a method for objectively evaluating FPC in the county to achieve a more rational use of farmland. For this purpose, the following study was conducted: (1) Taking winter wheat as the benchmark crop, annual multi-temporal RS images were used to estimate the per unit yield of winter wheat; (2) evaluating the FPC and analyzing the spatial distribution as well as instability; (3) analyzing the relationship between FPC and soil organic matter. We hypothesized that the farmland parcels with higher multi-year yields have better FPC and were relatively stable.

2. Study Area Description and Data

2.1. Study Area Description

The study area, Gaocheng county (37°51′–38°18′44″ N and 114°38′45″–114°58′47″ E), is located in the southwestern Hebei Province, China (Figure 1). It is located in the south–central part of Hebei Plain at the eastern foot of the Taihang Mountains, which is a typical winter wheat–corn rotation area. There is a warm-temperate semi-humid continental monsoon climate with hot summers and cold winters and four distinct seasons. The average annual temperature is 12.5 °C, and the annual precipitation is 494 mm. The soil type in the study area is mainly brown soil and tidal soil, and the soil texture is dominated by sandy and silt soils, accounting for about 80%, followed by clay soil. The average content of soil organic matter is around 27 g/kg. The study area is characterized by a predominance of wheat in the spring and maize in the summer, with a total cultivated area of about 549 km²; is a large grain-producing county in Hebei Province. In the southwestern part of the study area there are pear trees, and their phenological characteristics differ greatly from those of winter wheat and maize.

2.2. Data Description

2.2.1. Remote Sensing Data

The freezing damage caused a generally low yield of winter wheat in 2010. Considering that the yield loss in individual years was not conducive to the objective evaluation of FPC, we used the yield of winter wheat from 2009 to 2019 but excluded 2010 to evaluate FPC.

Annual multi-temporal satellite images with medium resolution were used to estimate the yield of winter wheat from 2009 to 2020, including Landsat-5, Landsat-7, Landsat-8, Sentinel-2, HJ-1A and GF-1, as shown in

Table 1. Acquisition dates of the RS images.

Satellite	Period	Year	Satellite	Period	Year
Landsat5	6 April 22 April 8 May	2009	GF-1	26 March 14 April	2015
			Landsat7	7 April 23 April
Landsat5	27 March 12 April 28 April	2011	GF-1	16 March 30 April	2016
Landsat7	4 April		Landsat8	9 April 25 April
Landsat7	6 April	2012	Sentinel-2	9 March 29 March	2017
HJ-1A	13 April 5 May		Landsat8	12 April 14 May
Landsat8	17 April	2013	Sentinel-2	14 March 18 April 28 April 8 May	2018
Landsat7	25 April
GF-1	10 May
GF-1GF-1	29 March 3 April	2014	Landsat8	17 March 2 April 4 May 20 May	2019
Landsat8	4 April

. The Landsat-5 MSS, Landsat-7 ETM and Landsat-8 OLI RS data with a resolution of 30 m, were sourced from the Geospatial Data Cloud website (http://www.gscloud.cn (accessed on 6 June 2022)). Sentinel-2 data with the resolution of 10 m and sourced from the European Space Agency website (https://scihub.copernicus.eu (accessed on 1 June 2022)). Furthermore, the 16m resolution of Gaofen-1 data and the 30 m resolution of HJ-1A data were sourced from the China Resources Satellite Application Center website (http://www.cresda.comhttp://www.cresda.com (accessed on 25 May 2022)). The combined datasets formed a continuous time series from 2009 to 2019. The winter wheat in the study area was in the peak growth period from March to May. During this period, at least three periods of images were selected per year, a total of 36 images. The RS images in the study area during the period were selected as the basic data for feature identification in that year. The image acquisition dates are shown in Table 1.

2.2.2. Farmland Parcel Data

Farmland parcel data could be used to avoid errors in image interpretation in the whole region and ensure the consistency of boundaries for image interpretation in different periods. In this study, Google Earth images with the resolution of 0.5 m were used to extract farmland parcel data via artificial digitizing. Taking full advantage of the high spatial resolution characteristics of Google Earth images, the farmland boundary was obtained by visual interpretation, the boundaries of farmland parcels were manually outlined on the image and saved as a vector in the ArcMap 10.2 software (Figure 2).

2.2.3. Field Samples of Winter Wheat

In this study, the field samples of per unit yield of winter wheat per year during ten years were used for yield estimation modeling. The samples were evenly distributed in the study area, and the spatial location of samples was recorded by differential GPS sensor. The grain of winter wheat was dried, threshed, and then weighed. The per unit yield of each sample was calculated according to the actual sampling area. The distribution map of the field samples is shown in Figure 3.

3. Research Methods

3.1. Definition of Farmland Production Capacity (FPC)

The definition of farmland production capacity is the actual food production within a certain period under normal technical and natural conditions.

To give the evaluation results of FPC the same meaning and achieve comparability within a county scale, it is necessary to select a benchmark crop to present regional standard grain yield. Since the county scale has a similar standard farming system and natural conditions, such as light, temperature and precipitation, it is practical to select the same crop as the regional standard grain yield in the study area. Referring to the agricultural land classification regulations issued by the state [26], the farming system in the study area is a two-cropping system every year, mainly including wheat–maize or wheat–cotton. Winter wheat was selected as the benchmark crop in this study.

3.2. Methodology

Figure 4 shows the process of evaluating FPC in the study area. The main steps were as follows.

(1)

Data pre-processing;

(2)

Calculation of NDVI for each image from 2009 to 2019 (excluding 2010) based on the band math;

(3)

The SVM classification method was used to extract winter wheat from the pre-processed images;

(4)

The estimation models of annual per unit yield of winter wheat were established by partial least squares regression (PLSR). The accuracy of the model was verified using the leave-one-out cross-validation method.

(5)

Constructing the model for estimating FPC based on multi-year yield.

(6)

Analysis of FPC level and instability.

3.2.1. Data Pre-Processing

The RS images from 2009 to 2019 (excluding 2010) were firstly pre-processed, including radiometric calibration, and atmospheric correction. The Landsat-7 ETM + sensor malfunctioned in May 2003, which led to stripe phenomena on the images since then. Therefore, the Landsat-7 data were processed using differential stripe repair. The Sentinel data used in the study were L2A products that were geometrically corrected and radiometrically calibrated. The atmospheric correction of Sentinel 2A image was realized with the Sen2Cor atmospheric correction model of the ESA’s official SNAP software. Subsequently, the NDVI was calculated in the ENVI5.3 software. The calculation formula is as follows:

$$\mathrm{NDVI}=\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}}$$

(1)

where NIR is the reflectance of near-infrared band, and R is the reflectance of visible red band.

3.2.2. Extraction of Winter Wheat Planting Area

The remote sensing images used for mapping the winter wheat were collected in March, April and May, corresponding to the spring greenup stage, the jointing stage and the grain filling stage of winter wheat. Due to the simple planting structure, there are few confused crops, and wheat is the main food crop in the study area. The support vector machine (SVM) classifier was used to map annual winter wheat, and the classification accuracy was verified using the field samples.

The transition matrix samples was constructed to evaluate the accuracy between 2009 and 2019 (excluding 2010), including overall accuracy and Kappa coefficient.

3.2.3. Establishment and Validation of the Model of Estimating per Unit Yield of Winter Wheat

The algorithm of partial least squares regression (PLSR) was used to establish the model of estimating per unit yield of winter wheat. PLSR can integrate the advantages of multiple linear regression, principal component analysis and least square regression.

A multiple regression model was established with the field sample of per unit yield and multi-temporal NDVI of the farmland parcel. The NDVI represented the growth status of crops during the key growth stages.

$$Y=a*\overline{NDV{I}_1}+b\ast \overline{NDV{I}_2}+c\ast \overline{NDV{I}_3}+d$$

(2)

where Y is the per unit yield of the parcel. The a, b, c and d are regression coefficients. The $\overline{NDV{I}_1}, \overline{NDV{I}_2}, \overline{NDV{I}_3}$ are NDVI of the three key growth stages of winter wheat.

In the follow-up, the leave-one-out cross-validation method is used to evaluate the model accuracy. One of the k samples was selected as the test sample, and the rest of the samples are used for training the model, repeated k times. This method has a high sample utilization rate. It can also establish a more comprehensive evaluation model in the case of a small amount of data.

The prediction accuracy of the model is explained by two evaluation indexes: stability and prediction ability. The stability is tested by the coefficient of determination R², and the closer R² is to 1, the better the stability of the model. The prediction ability is tested by the RMSE of the measured value and the predicted value. The smaller the RMSE, the better the prediction ability of the model and the higher the accuracy. The calculation formulas are as follows:

$${\mathrm{R}}^2=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2}$$

(3)

$$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}$$

(4)

where ${\mathrm{x}}_{\mathrm{i}}$, ${\mathrm{y}}_{\mathrm{i}}$, $\overline{\mathrm{x}},\overline{\mathrm{x}}$ are the measured value, estimated value, measured average value, and estimated average value (kg/ha) of winter wheat yield in the plot unit, and n is the number of samples in the subset of field yield measurement verification.

3.2.4. Construction of FPC Estimation Model

In this study, taking farmland parcel as the basic unit, the mean value of multi-year yield was used to present FPC, and the standard deviation (SD) of the multi-year yield was used to present the instability of FPC, so as to construct the FPC estimation model.

$$\mathrm{FPC}=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Y}}_{\mathrm{i}}^{\prime }}{\mathrm{n}}$$

(5)

$$\mathrm{Instability}=\sqrt{\frac{1}{\mathrm{n}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\prime }-\mathrm{FPC}\right)}^2}$$

(6)

where i is the parcel number, ${\mathrm{Y}}_{\mathrm{i}}^{\prime }$ is the standardized yield of this year, and n is the numbers of years.

Due to the differences in meteorological conditions in different years, the per unit yield of each parcel is incomparable. The yield of farmland parcels was standardized year by year as the following formula.

$${\mathrm{Y}}_{\mathrm{i}}^{\prime }=\frac{{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\min }}{{\mathrm{y}}_{\max }-{\mathrm{y}}_{\min }}$$

(7)

where i is the parcel number, ${\mathrm{Y}}_{\mathrm{i}}^{\prime }$ is the standardized yield of this year, ${\mathrm{y}}_{\mathrm{i}}$ is the yield, ${\mathrm{y}}_{\max }$ is the maximum of per unit yield in the study area, and ${\mathrm{y}}_{\min }$ is the minimum of per unit yield in the study area.

The distribution map of winter wheat was used to mask the images to avoid the interference of other features in yield estimation. Subsequently, combined with the yield estimation model, the per unit yield of each wheat pixel was obtained by band math in ENVI5.3. Based on the boundary of farmland parcels, the per unit yield of wheat parcels was obtained by zonal statistics.

To directly reflect the change in FPC, a grading method was proposed by using a double-threshold division strategy of partial–normal statistical theory [27].

FPC was classified into four grades: [${\mathrm{FPC}}_{\min }$, ${\mathrm{FPC}}_{\mathrm{mean}}$ − ${\mathrm{FPC}}_{\mathrm{SD}}$], [${\mathrm{FPC}}_{\mathrm{mean}}$ − ${\mathrm{FPC}}_{\mathrm{SD}}$, ${\mathrm{FPC}}_{\mathrm{mean}}]$, [${\mathrm{FPC}}_{\mathrm{mean}}$, ${\mathrm{FPC}}_{\mathrm{mean}}$ + ${\mathrm{FPC}}_{\mathrm{SD}}$], ${\mathrm{FPC}}_{\mathrm{mean}}$ + ${\mathrm{FPC}}_{\mathrm{SD}}$, ${\mathrm{FPC}}_{\max }$].

The instability of FPC was divided into four grades: [${\mathrm{Instability}}_{\min }$, ${\mathrm{Instability}}_{\mathrm{mean}}$ − ${\mathrm{Instability}}_{\mathrm{SD}}$], [${\mathrm{Instability}}_{\mathrm{mean}}-{\mathrm{Instability}}_{\mathrm{SD}}$, ${\mathrm{Instability}}_{\mathrm{mean}}$], [${\mathrm{Instability}}_{\mathrm{mean}}$, ${\mathrm{Instability}}_{\mathrm{mean}}$ + ${\mathrm{Instability}}_{\mathrm{SD}}$], ${\mathrm{Instability}}_{\mathrm{mean}}$ + ${\mathrm{Instability}}_{\mathrm{SD}}$, ${\mathrm{Instability}}_{\max }$].

4. Results

4.1. Extracting Winter Wheat planting area

Based on the above process, the SVM method was used to extract the winter wheat from 2009 to 2019 (excluding 2010). The accuracies of the annual classification results are shown in

Table 2. Annual classification accuracy of annual winter wheat.

Year	Accuracy of Land Use Classification
	Overall Accuracy (%)	Kappa Coefficient
2009	91.60	0.83
2011	93.48	0.89
2012	94.85	0.90
2013	92.68	0.85
2014	93.87	0.90
2015	92.16	0.84
2016	93.74	0.89
2017	92.67	0.87
2018	93.75	0.88
2019	87.49	0.80

.

The annual overall accuracies of winter wheat were between 87.49–94.85%, and the Kappa coefficients were between 0.80–0.90. The distribution of winter wheat could be used as the basic data for subsequent processing.

4.2. Estimating the Annual per Unit Yield of Winter Wheat

In this study, the NDVI from March to May and filed samples were analyzed by multiple linear regression, and the optimal linear regression equation and determination coefficient (R²) were shown in

Table 3. Yield estimation model based on long time series.

Years	NDVI Yield Estimation Model Equation	R2
2009	$y=-49.644+8545.3935\times x_1+8963.838\times x_2-6158.8935\times x_3$	0.53
2011	$y=-54.7495-10954.4295\times x_1+9109.2765\times x_2-3990.636\times x_3+14474.1975\times x_4$	0.93
2012	$y=-1122.576+10028.352\times x_1-1512.6435\times x_2+4086.0495\times x_3$	0.67
2013	$y=3193.9125-6666.6945\times x_1-1400.4615\times x_2+13142.172\times x_3$	0.43
2014	$y=6509.064+771.51\times x_1-1229.0955\times x_2+4350.2625\times x_3$	0.78
2015	$y=-4316.8935-2460.1695\times x_1-6045.366\times x_2+21888.366\times x_3+1698.5115\times x_4$	0.54
2016	$y=9698.499-857.376\times x_1+10216.3425\times x_2+12635.7495\times x_3-21806.481\times x_4$	0.89
2017	$y=323.097-3026.3985\times x_1+2182.1115\times x_2-5252.979\times x_3+14111.562\times x_4$	0.66
2018	$y=4857.9135+2323.3875\times x_1+141.237\times x_2-3725.9925\times x_3+3070.374\times x_4$	0.68
2019	$y=-1908.414-3921.096\times x1+6617.8695\times x2+13109.1345\times x3-881.781\times x_4$	0.76

. Among them, the stability of the model was highest in 2011 with R² = 0.93 and lowest in 2013 with R² = 0.43.

The leave-one-out cross-validation method was used to validate the models. The estimated and measured values of the modeling samples and testing samples from 2009 to 2019 (excluding 2010) were concentrated near the 1:1 line (Figure 5). Among them, the RMSE of testing samples was 368.1 kg/ha in 2011, combined with the determination coefficient R² = 0.93 of the modeling samples, indicating that this year has the best stability and predictive ability with the highest accuracy. It was verified by ten years of per unit yield estimation (Figure 6), the R² of the modeling sample was 0.87 and the RMSE of the testing sample was 395.82 kg/ha. and the yield estimation model could be used as a follow-up.

Using the yield estimation model equation, the ten-year yield estimation map of the study area was obtained after normalizing the data from 2009 to 2019 (excluding the 2010) (Figure 7). Combined with the distribution map of townships in Figure 1, it could be seen that the highest yield is 10,735.5 kg/ha, and the lowest yield is 4054.5 kg/ha. From 2009 to 2019 (excluding the 2010), the per unit yields of Zengcun, Xiguan, Nanying and Meihua towns were higher than the others, while those of Zhangjia zhuang, Nanmen, Qiutou and Xing’an towns were slightly lower. The distribution of wheat in Jiumen Hui, Nandong, Gangshang and Lianzhou towns was uneven, where the per unit yield varied greatly from year to year.

4.3. Evaluation of Farmland Production Capacity

By using the double-threshold division method, the FPC and instability grading results were obtained from the per unit yield of winter wheat from 2009 to 2019 (excluding 2010).

The FPC and the instability of each farmland parcel were analyzed (Figure 8), which basically conformed to the normal distribution. The Pearson correlation coefficient was −0.483 (p < 0.01), which showed a significantly negative correlation between them. In general, the trend shows that the larger the relative FPC value of the farmland parcel, the smaller the corresponding instability.

The FPC in the study area was divided into four grades (shown in Figure 9a,

Table 4. Area statistics corresponding to FPC grades.

FPC	Area Percentage (%)
Low	17.78
Moderate	28.71
High	35.49
Very high	18.02

). The FPC in the north and south of Gaocheng county was higher, while the central region was lower. Combined with the distribution map of the town (Figure 1), it could be seen that the areas with high FPC accounted for 35.49%, mainly concentrated in Zhangjia zhuang, Xing’an and Lianzhou Towns. The areas with very high FPC accounted for 18.02%, mainly concentrated in Zengcun, Xiguan, Nanying and Meihua Towns. The areas with low and moderate FPC accounted for 17.78% and 28.71%, respectively, mainly staggered in Jiumen Hui Township, Nan Dong, Chang’an and Gangshang towns.

The instability of FPC from 2009 to 2019 (excluding 2010) was analyzed (Figure 9b, shown in

Table 5. Area statistics corresponding to FPC instability.

FPC Instability	Area Percentage (%)
Most stable	14.63
Moderately stable	41.84
Unstable	27.30
Most unstable	16.23

). On the whole, the stabilities of FPC in the north and south of Gaocheng were moderately stable and the most stable, while those in the central region were unstable. Among them, moderately stable areas accounted for 41.84% of the total area, and these areas were distributed throughout the county, mainly concentrated in Zengcun, Zhangjia zhuang, Qiutou, Nanying and Meihua Towns. The most stable areas accounted for 14.63% of the whole area, mainly concentrated in Xing’an, Xiguan and Meihua Towns. The areas where FPC were unstable and most unstable accounted for 27.30% and 16.23%, respectively. These areas were scattered in Jiumenhui Township, Gangshang and Nandong Towns.

The spatial distribution of SOM in Gaocheng could be obtained by spatial interpolation of 450 soil samples (Figure 10). The SOM content was between 12.96–36.82 g/kg, and the low-value areas were mainly distributed in the middle and southeast, and the remaining areas were the middle and high values.

The analysis of SOM and FPC (Figure 11) showed a significant positive correlation, with a Pearson correlation coefficient of 0.525 (p < 0.01), indicating that SOM and FPC have a high correlation. Soils with a high organic matter content have a relatively high soil temperature, good insulation, and smooth and long-lasting fertility. Usually, the organic matter content in soil is positively correlated with the level of soil fertility within a certain content range under the similar other conditions. The SOM content in the central and southeastern regions of Gaocheng was low, and the soil fertility was low compared with other areas, so the per unit yield of crop was lower, and the FPC level was relatively lower.

5. Discussion

In this study, long time series of RS images were used to estimate the per unit yield of annual winter wheat by establishing regression models between NDVI and field samples. Taking winter wheat as the benchmark crop, a double-threshold division strategy was applied to evaluate the FPC at the county scale.

Currently, most of the studies that focused on RS to monitor productivity changes of farmland using MODIS images [19]. Due to the low spatial resolution of MODIS images, this often leads to the situation of ‘same spectrum and different objects’ and ‘same object and different spectrum’. Using multi-temporal and multi-source RS data with medium-resolution has a positive effect on solving this problem. The medium-resolution spectral image can obtain rich spectral information of ground targets to achieve a high recognition accuracy for crops. Meanwhile, multi-temporal and multi-source RS data can complement redundant information, which improves the reliability and capability of image interpretation in crop identification and extraction. In this study, long time series of multi-source RS images with medium resolution were used to obtain rich spectral information on wheat at critical growth stages, which could effectively monitor the growth of wheat and facilitate the estimation of per unit yield, and then could evaluate the FPC.

Based on the medium resolution RS images, we estimated the per unit yield of wheat. Currently, NDVI is an important vegetation index for judging crop growth [28] and can reflect the growth status and growth environment of crops to a certain extent. Due to the high correlation between crop growth and per unit yield, NDVI could be used as one of the indicators for crop yield monitoring. However, the vegetation index at different growth stages showed different sensitivity to the per unit yield of field samples. In this study, the vegetation index in the three growth stages was selected. Compared with a single stage, the accuracy of the multiple regression models established by the NDVI in multiple stages were improved. However, crop yield was estimated in this study only through NDVI, which was widely used in vegetation remote sensing. When the canopy coverage was too high, the sensitivity of the vegetation index decreased [29], so other methods can be used to eliminate this disadvantage in the future.

The yield estimation methods used in the study of FPC have some differences from the traditional methods. The traditional methods for crop yield prediction are carried out at the pixel level by establishing the relationship between per unit yield and the NDVI. The method proposed in this study takes farmland parcel as the basic unit, instead of pixels. The per unit yield of each parcel was estimated by the relationship between the mean NDVI of parcel and field samples. Compared with pixel-level information, the yield information of farmland parcel level is more practical for agricultural managers.

The estimation of multi-year yield was used to evaluate the FPC. Compared with previous studies [6,7,8,9,10,11,12,13,14,15], this study focused on evaluating the grade of FPC at the county scale. FPC is affected by natural and social conditions [30,31]. Until now, there is no unified standard for evaluating FPC based on impact factors. This study was conducted with long time series during the key growth stages of crop. Taking the farmland parcel as the basic unit, for many years, the per unit yield of benchmark crop was used to evaluate the FPC and reveal its spatial and temporal variation. It was a rapid evaluation method of FPC at the county scale. The method of evaluating FPC has a strong adaptability to the areas with flat terrain and relatively uniform crop planting. At the county scale, solar radiation, temperature and precipitation have little impact on spatial differences in FPC. The SOM was considered as a factor to ensure the persistence and stability of crop productivity, and a positive correlation between SOM and productivity was demonstrated [32]. This study also proved that there was a significant positive correlation between the FPC and SOM, which provided an important basis for explaining the spatial differences of FPC. However, there are many factors affecting the FPC that need to be further explored in follow-up research.

6. Conclusions

In this study, with the support of a 10-year long time series of RS images, the multi-temporal NDVI in the rapid growth period (from regreening stage to jointing stage) was used to estimate the per unit yield of annual winter wheat. By integrating the multi-year mean yield and interannual variability of winter wheat, the model of evaluating FPC was developed. Through double-threshold division strategy, the grades of FPC in the study area were divided and mapped. The conclusions were drawn as follows.

(1) Winter wheat from 2009 to 2019 (excluding 2010) was extracted based on the SVM method; its overall accuracy was between 87.49–94.85%, and the Kappa coefficient was between 0.80–0.90. The stability and predictive ability of the per unit yield estimation model were good.

(2) In terms of FPC and instability, on the whole, the FPC in the south and north of Gaocheng were high or very high in the stable or the most stable area, while the FPC in the center was moderate or low in the unstable area.

(3) The SOM is significantly and positively correlated with the grades of FPC, with a Pearson correlation coefficient of 0.525 (p < 0.01).