*2.2. Methods*

The geometric method was used to implement the TMA model. The geometric method is an important method for mixture analysis, and from a geometric perspective, the multidimensional images can be viewed as a convex simplex. The convex geometry method [42] was introduced to construct the simplex structure of time series remote sensing data in the feature space, and the endmembers were found in this feature space.

The major steps of the methodology, including feature selection, feature space construction, endmember selection, cropping intensity estimation and validation, are presented in the flowchart (Figure 3).

#### 2.2.1. Feature Selection

Intra-annual time series remote sensing images provide land surface phenological information and reveal spatio-temporal development of vegetation [43]. The EVI profiles of different land-cover types demonstrated the unique phenological characteristics of doublecropping, single-cropping, evergreen forests, deciduous forests, water bodies, built-up areas, etc. (Figure 4). The temporal profiles of crops are obviously different from those

of other land-cover types. Moreover, there are great differences between single-cropping and double-cropping. There are two peaks for double-cropping, one is around DOY (day of year) 065 to 097, and the other is around DOY 193 to 225. However, there is only one peak for single-cropping, which is around DOY 177 to 209. Similarly, there is only one green cycle for forests, but the green cycle is much longer and wider compared to that of single-cropping. In addition, both water bodies and built-up areas have low EVI values throughout the year. These phenomena make recovering cropping intensity information from time series remote sensing data possible.

**Figure 3.** Flowchart of the TMA method.

**Figure 4.** EVI profiles of major land-cover types in Hubei province. A total of 3000 samples were collected to generate EVI profiles, including 537 of double-cropping, 622 single-cropping, 486 evergreen forests, 432 deciduous forests, 517 water bodies and 406 built-up areas.

Principal component analysis (PCA) has been proven to be effective at detecting seasonal changes in vegetation when applied to the time series vegetation index [44]. PCA transformation projects original data into new k-dimensional components ordered by variance, with the majority of information provided by the first several components. PCA components have geographic meanings; for example, Henderson et al. [45] found the components corresponding closely to typical vegetation density or degree of seasonality, Wang et al. [46] found the components coinciding with the average normalized difference vegetation index (NDVI) (PCA component 1) and accounting for the most prominent man-induced vegetation alterations (PCA component 2).

PCA transformation was applied to the original time series MODIS EVI to obtain components with geographic meanings while reducing feature dimensions. In this study, the first three components reserved 93.18% of the original information. From PCA component 1 (PCA 1), vegetation and non-vegetation (water bodies and built-up areas) could be easily distinguished, and the difference between natural vegetation and croplands was also very significant (Figure 5a,b). PCA component 2 (PCA 2) could discriminate double-cropping from other land-cover types, and the difference between double-cropping and single-cropping was also very obvious (Figure 5c). Moreover, PCA component 3 (PCA 3) could discriminate

single-cropping from other land-cover types (Figure 5d). Therefore, the combination of the first few components could be used to discriminate the major land-cover types.

**Figure 5.** Land-cover types (**a**) and the first three PCA components of the time series EVI, (**b**) PCA 1, (**c**) PCA 2 and (**d**) PCA 3.
