2.2.3. Cropping Intensity Estimation

The LSMA model was used to implement the TMA method. The fully constrained LSMA model was used to estimate the abundance of each endmember. The unmixing was conducted in the time dimension by replacing the original spectral information with multi-temporal vegetation indices. The linear unmixing method assumed that the EVI temporal spectra of a pixel are a linear combination of each endmember. The formulas of linear spectral unmixing (1) and constraints (2) and (3) are as follows:

$$EVI\_{i} = \Sigma\_{j=1}^{n} \left( f\_{j} EVI\_{i,j} \right) + \varepsilon\_{i} \tag{1}$$

$$
\Sigma\_{j=1}^n f\_j = 1 \tag{2}
$$

$$0 \le f\_i \le 1 \tag{3}$$

where *EV Ii* is the EVI value for each phase *i* in the temporal EVI image, *n* is the number of end members, *fi* is the fraction for each end member *j*, *EV Ii*,*<sup>j</sup>* is the EVI value of endmember *j* in phase *i* (also the abundance of each endmember), and *ε<sup>i</sup>* is the residual.

The abundances of all endmembers were under the constraint of being non-negative and added up to 1. The abundance of double-cropping was extracted and was regarded as cropping intensity, in which pixel value 0 represented abandoned cropland, and pixel value 1 represented homogeneous double-cropping areas.
