**1. Introduction**

Yield potential (Yp) is the upper limit of the yield of a specific crop type within a given domain and is limited by only the local heat and light resources [1]. Narrowing the gap (yield gap, Yg) between Yp and on-farm yield (Ya) is critical for increasing food production. Yg is caused by multiple factors, but not all could be controlled [2,3]. Factors contributing to Yg were categorized into either persistent (field managements, terrain, and soil quality) or non-persistent factors (adverse climate, insect attack, and other non-managemen<sup>t</sup> factors) by Lobell, et al. [4]. The persistent factor, field management, could be controlled in the field and has made considerable contributions to Yp, as presented in previous studies [2,5,6]. Therefore, the knowledge of Yp and the contributions of persistent factors to Yg can provide useful information for improving crop yield.

Sowing date (SDT) is one of the important managemen<sup>t</sup> factors that affect crop yield [7–9]. A few economic inputs are required to optimize SDT on a farm. Several

**Citation:** Zhang, S.; Bai, Y.; Zhang, J. Remote Sensing-Based Quantification of the Summer Maize Yield Gap Induced by Suboptimum Sowing Dates over North China Plain. *Remote Sens.* **2021**, *13*, 3582. https:// doi.org/10.3390/rs13183582

Academic Editors: David M. Johnson and Jose Moreno

Received: 7 June 2021 Accepted: 5 September 2021 Published: 8 September 2021

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**Copyright:** © 2021 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/).

methods may be available for exploring Yp and quantifying the contribution of this factor to Yg. These methods could be generally categorized into two types: model simulation and field experiments. The latter method provides an estimate of Yp and other levels of yield under controlled experimental conditions, thus it can quantify the effect of SDT on Yg [10]. However, for analysis over a wide spatial or temporal range, such a method is time-costing and uneconomical. In this case, the field experiment generally served as a means of acquiring data for calibrating and validating crop growth models (CGMs) [11–13]. Model simulation is favored for its low cost and high efficiency [1,14]. CGMs such as the agricultural production system simulator (APSIM) [15], crop environment resource synthesis (CERES) models [16], and CSM-IXIM [17], after being calibrated, can produce reliable estimates of crop Yp and Ya and can also simulate crop yield under controlled conditions [11,18,19]. The knowledge of the contribution of managemen<sup>t</sup> factors, including SDT, to Yg could be revealed by comparing simulated values of crop yield under different managemen<sup>t</sup> scenarios [6,20]. However, quantifying the contribution of SDT to Yp is not feasible over a broad region using CGMs owing to the inaccessibility of spatiotemporally continuous field managemen<sup>t</sup> information and the sparse spatial distribution of accessible meteorological sites at present. Simulations and analyses with CGMs in existing literature were merely performed on meteorological-site levels or within a small region and provided limited information for understanding Yp and Yg in space [6,20].

The use of remote sensing (RS)-based methods may be an alternative way to address the above issues, as the use of RS data can make a model less dependent on meteorological data and managemen<sup>t</sup> information and show better performances in regional simulations [21,22]. Unlike CGMs, the key factor, leaf area index (LAI), for simulating photosynthesis rate RS-based models is remotely sensed rather than simulated by the model [23], which makes RS-based models more applicable to regional applications. An RS-based land process model has long been used to simulate ecosystem productivity and is also useful for simulating crop yield [23,24]. SDT, which is also an essential input of RS-based models to map crop yield, can be obtained by analyzing the RS vegetation indices (VI) time series [25–27]. Hence, we can use RS data to study the contribution of suboptimum SDT to Yg over a broad region. Vegetation parameters retrieved from RS data reflect the actual growing condition of crops and seem to be useful for simulating only Ya. However, spatiotemporal variations in pixel-level Ya predicted using an RS method are potentially useful for quantifying Yp [28] and understanding the contribution of different factors to Yg [2,29]. Assuming that potential yield is realized on a local scale, pixel-level Yp could be computed as the high percentile (95th or 99th) of yield distribution of surrounding pixels [28,30]. To avoid this assumption, Lobell [28] suggested using a hybrid method that estimates the real Yp by fitting the Yp derived from the above RS-based method to the estimate of a calibrated CGM. However, the hybrid approach may in turn be restricted by CGMs' high input data requirement over a broad region. In addition, such a method may fail when Yg and factors contributing to Yg varied significantly and irregularly in space. Therefore, an RS-based method to quantify regional-scale Yp, Yg, and the effect of SDT on crop yield, without the need for CGMs, is needed.

Multiple types of satellite data are available for modeling crop yield and Ygs. Highspatial-resolution data, such as Landsat and SPOT, that have relatively long revisit times have been generally used to develop empirical relationships between crop yield and spectral indices at a specific developmental stage of the crop [29,31–33]. These empirical methods are limited to quantify Yp and Yg for regions with lower levels of field management [28]. Besides, these methods do not explicitly consider the effect of SDT on crop yield, being not able to quantify the SDT to Yg. The two Sentinel-2 satellites (Sentinel-2A and B) can provide 10 to 20 m resolution multispectral data with a revisit period of 4–5 days and are useful for driving a process-based model to estimate crop yield, which requires time-continuous inputs [34]. However, Sentinel-2B data were only available from 2018 when the satellite was launched; hence, using process-based methods with Sentinel-2 data to reproduce Yg and Yp from earlier years is impossible. Although the widely used

MODIS data have a coarser spatial resolution than Landsat, SPOT, and Sentinel-2, it can provide time-continuous images with more available pixels in time and are available from 2000 to present. The data have also been used to estimate crop yield with process-based models [23,35].

In this study, we aim to develop a new RS approach that uses MODIS data to quantify Yp and the contribution of suboptimum SDT to Yg of summer maize over the North China Plain (NCP), with three main objectives: (1) To develop a novel RS-based method driven by MODIS data to simulate Yp and Yg at a large spatial scale; (2) to assess the reliability of the developed RS-based method in simulating Ya and Yp over the NCP; and (3) to quantify Yg and the contribution of suboptimum SDT to the Yg of summer maize over the NCP in the period 2010 to 2015.

#### **2. Materials and Methods**
