**1. Introduction**

Early estimates of crop yield will contribute to addressing the key issues of crop production management, future market output, and deep processing. According to the early prediction of crop yield, farmers can adjust and optimize irrigation decision making in a timely way to maximize yield for enhancing profits, while policymakers also take reasonable measures to deal with potential trade risks in order to safeguard food security and ensure market stability [1]. It should be emphasized that the earlier yield forecasting information is provided, the more effective measures are likely to be undertaken [2].

Plentiful studies have been implemented to predict final yield in the past decades based on different methods including field survey, statistical methods, and crop growth

**Citation:** Chang, H.; Cai, J.; Zhang, B.; Wei, Z.; Xu, D. Early Yield Forecasting of Maize by Combining Remote Sensing Images and Field Data with Logistic Models. *Remote Sens.* **2023**, *15*, 1025. https://doi.org/ 10.3390/rs15041025

Academic Editors: Kenji Omasa, Shan Lu and Jie Wang

Received: 9 January 2023 Revised: 10 February 2023 Accepted: 10 February 2023 Published: 13 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

models [3–5]. Field survey can assess yield by capturing the ground truth; nonetheless, it is highly time-consuming and labor-intensive. The core of statistical methods lies in the acquisition of empirical relationships between crop yields and specific related indicators. Despite reasonably accurate results in specific field areas, it is restricted when scaling up this relationship to large areas. Crop growth models can be applied to describe plant dynamic growth. Biomass is a critical biophysical indicator with a close link to yield at harvest. Therefore, one way to predict yield is to acquire biomass estimates via crop growth models and then implement the in-season evaluations of yield on account of their good correlations. Crop growth models include process-based models and experiment regression ones [6]. The former requires many parameters as inputs [7,8], making it difficult to execute the models in data-scarce regions [9] though it is more mechanistic than the latter. In contrast, with only a few parameters, statistical regression models have been developed (e.g., the Richards, Compertz, and Weibull equations) and continue to be widely used to illustrate crop growth dynamics including biomass [10–12], but this method has the limitation of extending model parameters to large areas.

Given that these methods have limitations, data assimilation has been developed to solve these problems in yield forecasting. Intrinsically, data assimilation is used to incorporate observations into the model to obtain the optimal possible estimates [13]. The rapid advancement of satellite images allows for large-scale crop growth monitoring [14,15]. Numerous studies have shown that incorporating remote sensing data into crop models can improve regional yield estimates [16–18]. The research has focused mainly on the assimilation of mechanism models [2,19–21] despite the fact that they require numerous input parameters. By contrast, it is worth investigating the potential of experiment regression models in early-season yield forecasting for large areas via data assimilation when there is a lack of detailed input information.

As one of the most important crops, maize yield forecasting is critical for the development of agriculture and livestock [22] and can serve as an excellent reference for other crop research. For different purposes, farmers can harvest maize as silage or grain yield, and correspondingly, dry biomass accumulation (DBA) and fresh biomass accumulation (FBA) need to be predicted as an important precondition for yield forecasting.

The logistic model is one of the most commonly applied regression models for crop growth processes such as DBA throughout the growing season [23–27]. However, the logistic model fails to fully describe the development process of FBA or leaf area index (LAI) due to the existence of a downtrend process after the milk stage caused by leaf senescence. A revised logistic model proposed by Wang [28] overcame this limitation and performed well when describing LAI changes [29], but it has not yet been used for FBA. In addition, the logistic model was originally developed for individual plants that neglected regional applicability. Elings [30] acquired maize leaf area dynamic growth in various environments using a set of parameters for the data normalization method. This method has been used to establish a normalized logistic model of relative DBA (RDBA) for simulating regional crop growth patterns [4,31].

Indeed, another major obstacle to the application of the logistic model in region is the choice of input parameter, which serves as a vital bridge linking the point-based and regional applications. Furthermore, previous studies have demonstrated the growth curve of maize using the logistic models with air or soil temperatures as input [32–34]. The cropping environment is the most influential factor in plant yield [35,36]. Canopy temperature (Tc) is obviously a better indicator for reflecting crop water message responses to field conditions. Moreover, Tc can be considered as matched to land surface temperature (LST) in large agricultural areas, which can be inversed from remote sensing images [37]. Therefore, integrating LST data into the normalized logistic models can acquire the values of RDBA in combination with the once-measured DBA on a certain date and harvest index (HI), which presents an opportunity to achieve early yield forecasting in regions.

Therefore, an approach was developed to retrieve early prediction of maize yield using logistic models in combination with daily LST images and in-season field observations. The major objectives are as follows: (1) to calibrate and validate the corresponding logistic models for simulating the maize growth curves including RDBA and relative FBA (RFBA) based on different independent variables including temperatures of air, canopy, and soil at 20 cm or 40 cm in the root zone; (2) to determine the applicability of Tc in crop monitoring as well as the appropriate model parameters; (3) to forecast maize yield in region by HI and biomass maximum including DBA and FBA, which can be acquired by incorporating the normalized LST from remote sensing as an approximation of the normalized Tc into the corresponding optimal models with once-observed DBA or FBA as the driving force; and (4) to test the portability of this approach by producing grain yield maps in other agricultural districts and comparing them to local observations.

## **2. Materials and Methodology**

#### *2.1. Study Areas*

The first study region was in Changchun area, Jilin Province (about 2.05 million ha), as shown in Figure 1a,b. This region was characterized by a northern temperate continental monsoon climate, with an average annual rainfall of 520–755 mm [38], of which more than 60% occurs in the summer. The annual average daily temperature is 4.8 ◦C, and the sunshine duration is approximately 2700 h. The data for model developments were obtained from field experiments of maize growth (May–September) from 2017 to 2019 in an agricultural research station (43◦38 39.92N, 125◦19 7.77E, 248 m a.s.l.) near Changchun city, as shown in Figure 1f (about 73 ha). The maize cultivar was Xianyu 335. The predominant soil types are black and meadow soil, and the soil texture is mainly sandy loam soil. The field capacity (Fc) and wilting point (Wp) were measured as 37% and 16% in an 80 cm average of the crop root zone, respectively. Precipitation and soil water content in 2017–2019 were monitored, revealing an optimal soil moisture range for maize growth (Figure 2).

Another study region for this work was the Jiefangzha sub-irrigation district (approximately 0.229 million ha), which is one main component of Hetao irrigation district in Inner Mongolia, China (Figure 1a,c). Maize is one of the major crops in this region. The yearly average daily temperature is 9 ◦C, with an annual rainfall of approximately 151.3 mm. The field monitoring system was conducted in the Shahaoqu experimental station in 2016, as shown in Figure 1b (40◦55 8"N, 107◦8 16"E, 1036 m a.s.l.). The values of Fc and Wp are 35% and 15% in the crop root zone, respectively. More information can be found in the report by Bai et al. [39].
