## 1 Introduction  
Maize, as the primary staple, plays a vital role in agricultural production in China. It is very significant to estimate the cultivated area of maize for national food security and sustainable economic development [1, 2]. Huanghuaihai Plain covers approximately 4.5% of the whole country, whereas the maize planting area accounts for about 30% of the total maize acreage, which is the main production areas of summer maize in China. The distribution of maize in this region affects grain policy making, adjustment of the cropping system structure, and academic studies related to maize in China [3, 4]. Therefore, there is an increasing need for objective, timely, and accurate estimation of the maize area over the Huanghuaihai Plain. As a kind of earth observation technology, remote sensing can effectively acquire the spatial distribution and spectral information of ground objects, with wide geographic coverage and the merit of large information capacity, high accuracy, and speed, which provides opportunities for crop identification [5; 6; 7; 8; 9]. Different crops have various spectral characteristics in remotely sensed images [10; 11]. The multi-temporal vegetation indices (VIs) reflect the changes in the spectral features of vegetation over time, which can discriminate different crop types [12; 13; 14; 15; 16]. Many previous research studies employed the multi-temporal VIs approaches to map the maize cultivated area. [PERSON] and [PERSON] used temporal normalized difference vegetation index (NDVI) data from 250 m moderate resolution imaging spectroradiometer (MODIS) images to classify the maize over the U.S. Central Great Plains [17]. [PERSON] et al. reconstructed a mid-scale time series NDVI dataset derived from the fusion of MODIS and thematic mapper (TM) images based on the wavelet transform to estimate the maize area in Yuanyang County of Henan Province [18]. [PERSON] and [PERSON] combined the temporal NDVI series and ancillary field data to map the maize area in the large-scale commercial farms of Zimbabwe though the maximum entropy method [19]. [PERSON] et al. adopted the identification method for spring maize based on spectral and phenological features derived from the MODIS land surface reflectance time series data in Northeast China [20]. In contrast, although these studies were valuable for the recognition of maize, there are still some challenges to be faced in mapping the spatial distribution of maize on a large scale due to the spatial variations of maize phenology. The spectral features of summer maize on remote sensing images are different at the same time, as the maize phenology varies in different regions. In order to weaken the influence of phenology differences on the accuracy of crop area extraction, some researchers have considered the influence of latitude on summer maize phenology, when using the multi-temporal VIs approach to map the maize area on a large scale. For example, [PERSON] et al. used the lag values of phenology change with latitude to modify the MODIS-enhanced vegetation index (EVI) time series curve of maize and mapped the spring maize in Northeast China [21]. [PERSON] et al. also considered the differences in maize phenology with latitude to discriminate the summer maize based on the multi-temporal MODIS EVI images over the Huanghuaihai Plain [22]. In both studies, the influence of latitude on crop phenology was taken into account when using multi-temporal MODIS images mapping the summer maize area on a large scale, which had improved the accuracy of maize area extraction. In fact, the phenology of summer maize is not only affected by latitude but also sensitive to the change in environmental conditions, as well as changes with the environmental variation. The maize phenology is sensitive to changes in environmental conditions, resulting in the maize phenology that would be altered by environmental variability [23; 24; 25; 26; 27; 28].